1. Akar-akar dari
adalah x1 dan x2. Jika x1 – x2 = 5, maka p adalah ...
a. -8
b. -6
c. 4
d. 6
e. 8
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggSjJPJ2GTs0d690jOYKH_etGwJvV6ewS__aE9d6K03Z9T51bpsAw9BWf77NIfO2Zq7D0mVKbT2AYP_z_ch6P_WqIah0qjlNbYl5Sd86KDbmvKMq5RCF59hzvddHL1quqp8AN6ZlbCfrM/s1600/a.png)
Pada soal diketahui PK:
dengan a = 2, b = -6, dan c = -p
x1 – x2 = 5, maka:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdaqljK-eVj07ju-uvaq4xDXVJbRBf4PIsRo2V3FaH7Sf0APX1hIv-2-LMLQ5VLOz9vQWwvQz2s4hArR-Vx_EtypmSx-vSEw1Ym42ydD7dtdjZRrVYmWemNZOL89_8nyz2LeMZEgBtOXc/s320/a.png)
100=36+8p
100 – 36 = 8p
8p = 64
P = 64 : 8
P = 8
Jawaban: E
2. Akar-akar persamaan kuadrat
adalah α dan β. Persamaan kuadrat baru yang akar-akarnya (α – 2) dan (β – 2) adalah ...
Pembahasan:
berarti a = 1, b = 2, dan c = 3
Akar-akar PK di atas adalah α dan β, maka:
α + β = -b/a = -2/1 = -2
α . β = c/a = 3/1 = 3
persamaan kuadrat baru dengan akar (α – 2) dan (β – 2) adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZLH1JJ0OMkQ5mJpVUd5QZ39F13fD4Y-HdJzv05Yfjf9oNf07kaRNoE0UKCRHxuZoA1T8qK89R2AVtnymi3AgWJ9EYcXLt8sw59RwBwf4fQ-J1GxJmNC_O7uQUGVP75QmCfwODDXyWPFA/s320/a.png)
Jawaban: C
3. Jika a dan b adalah akar-akar persamaan
maka persamaan kuadrat yang akar-akarnya -1/a dan -1/b adalah...
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4bkaIaGyXDCUpThB8XxP8Uw36YilQkbAJyED6FceH0KfEUHo6OwX83nsly-2-RN_4uAFCvGSTNvzwyO_ayX0XjxrtxTDXaOdtJnf4bVOJaitJhYlglbzljN77ktDSEUABJIkBiOBnSGc/s1600/a.png)
Pembahasan:
berarti a = 2, b = -3, dan c = -5
Akar-akar persamaan PK di atas adalah a dan b, maka:
a + b = -b/a = -(-3)/2 = 3/2
a . b = c/a = -5/2
persamaan kuadrat baru yang akar-akarnya -1/a dan -1/b adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgk72YRXnRJ34IPgih1tHHjg0TaUneA25A7WRmQFHUY7JKInPDfzI9FzAYQAP5RM75yAP5zeF8oU2Z3Yra6Wqmty4pIWVjmywWzvrePd_Aa9DCZAMkq4yE1zIPozAY7gns1hGw1LH-jZQk/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7JXKw_-gnNWUAw_7lqkK2j2U_cflVPSOKbI_THYlFzJyd2x_O9J4ZbzWWArYV1iIy7vjRA0GMVv8L548KpU3OU3qk29jFA85mMy8tuTqVAwxGRlfK5b1Ql6vDkIUxLgD7GVd1ZG-OxyQ/s1600/a.png)
Jawaban: D
4. Persamaan
mempunyai akar real sama, maka nilai p sama dengan ...
a. -3 atau 1
b. -1 atau 3
c. 1 atau 3
d. 1 atau -2
e. -2 atau 3
Pembahasan:
kalikan silang
, jadi a = 1, b = (-3 - p), dan c = 3 + 2p
Syarat sebuah persamaan memiliki akar real sama adalah D = 0
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTHx-EQYXFmSppXBRvyx5eiUlQUrveUBzK_h226AOJh5gHR4H5GNfJXrlGMMad-fc_W0_TbhP6KOABHDt4Kuxnh-mPeaeHuF_CmOUfsCNjO-EQA50Fkq4VGmKZ_13oOQbqChW3H_s6v8E/s1600/a.png)
(p-3)(p+1)=0
p = 3 atau p = -1
Jawaban: B
5. Jika x1 dan x2 akar-akar persamaan kuadrat
maka persamaan yang akar-akarnya
adalah...
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7aYvfDrCPanN5yX3hMIo-mdd_ek4SVCuIXdYKjbHzxeXgfk-N35K-BLr9dUxVUq4nriQYCv-EX_yWxxDI3KdPrGLoiSN9GTWeWWSdHO8oYdWDmK8dLGs_aX3WonFUFm5jzztqyVut-0M/s1600/a.png)
Pembahasan:
, berarti a = 2, b = 1, dan c = -2
PK di atas memiliki akar-akar x1 dan x2, maka:
x1 + x2 = -b/a = -1/2
x1. x2 = c/a = -2/2 = -1
PK baru dengan akar
adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEii1qmp5BKraopFK0Um3latTuRhyphenhyphenFenh4NwrX1f7ZrUWRJ0GcJfklFQICcD3QHXuMnfW3Y24dDjjejkHOb8B-084ocTURv44ANUKYd4XQ3hDRXrGCPJu_KbJ-yFVs2orQxjf4iY9fxYXPE/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUxMjx8KPz6wVWsxC6p5xq3rEWLc8JToEzR4dcmN0YdlpF0h2cB59z7bsWORXqtYrXEr8Kaoy72KBk2AEOPddiVd_lKltkq4xNj393RGTP4haoW-utfmKOARhdAqL9kLBUZnEIKvwl_B4/s1600/a.png)
Maka, PK yang baru:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0dXncqprdhH4QNPDbLX5l88EBPAlvhJb6TFOgG88FCa-dHMuNuRrdaB6U1wyxpb8DNGYBPfkbZjcjzdZuJUdbbhLzjPrzY3YUwgECLGSyCkt8D7Nu5LC6i88TyuXZjWywCAI6c0cj9p4/s1600/a.png)
Jawaban: B
6. Akar-akar persamaan kuadrat
, p > 0 adalah
. Persamaan kuadrat baru yang akar-akarnya
adalah ...
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkZ7qpNP0S-YwtHhRhxVAs80uSnDbHMj91fQcvyPnyF-FcWc9k_Mwk-_azRR7IUqNlu1frJuSPlyk86EC9AcLN37fgUMzC7bTzVsI6tPCOzm9HQa5DM4hJCqWifFmJwD-_MgMRvDdmCZE/s1600/a.png)
Pembahasan:
, a = 1, b = -p, dan c = 4
PK di atas memiliki akar
, maka:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-Tpef-t-nFrub-6WKtDf3Ska1STXTOISpxfkxZTyINPWTxnl05dRynIW9GmSMsfr6voBZk-BCX-5uag1MSPVG8-h9_ftSMYkHI7HkcXhOhe7CuWZj7oD4J3SVJYRjoTiIzF_GB9Gwl1w/s1600/a.png)
PK baru dengan akar
adalah...
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8-fKOB11ox1WIwKIklPNcPZkjwQMM_uS6x4lBQ099_SWoeEGWYyO7PsvUoLoj9QkjezZy9yh_HTT_3ijDUSylsedPafVJDR9w9cjB-qpKvMdptt7dgBClhfxzbNgDpYAN8X-v7iDX5Bc/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHTLToIUSx9vqx6KALPmzVX-NV6Jm8NCYshFgi6mSwXY3mKsfdIHBlwb9QTkOJ_Ovsic_LwEN4-lSybQHrxhO442eZV5mBSYj425-o6QBjSkuRSNWSs8Om4vO36KO0bCjr8HYzKYzuU7E/s1600/a.png)
PK yang baru adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTvRHs4DD9GhznkYGuK3pYo1JAHqERhWIomhFQS5OwrHPXD-Oj54CBCTJAyDIMBzcMZs8GEXK5MEWlx_aaoNIUphV12Q7XKLXvjYZ_Mb-umFgpi7gJuHLUHrszD3EHMozSerDX42AC8Us/s1600/a.png)
Jawaban: E
7. Jika jumlah kedua akar persamaan kuadrat
sama dengan nol, maka akar-akar itu adalah...
a. 3/2 dan -3/2
b. 4 dan -4
c. 5/2 dan -5/2
d. 5 dan -5
e. 3 dan -3
Pembahasan:
, a = 1, b = 2p – 3, dan c = ![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDU1jx3TRAxGNnq9HuvcyHUl1rba6I5N-5aUjVntcWzdBW-baQH_LnvbOGO7fsXiLch_byZ0N9VHqkH1M6LxzACbCzmpavXh64lZ-_7FaAjvHEU9c3xlWfsLAXLSL3MRVpMxcSWn8le2U/s1600/a.png)
x1 + x2 = 0
-b/a = 0
-(2p – 3)/1 =0
-2p + 3 = 0
2p = 3
p = 3/2
Maka PK di atas menjadi:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiKR6Dk6Uhqv-kTOfIX4LUnzQD_laxQKnM7xIbBTbK_3-i0zAi0wUXM8pY884AhxqF0ES3f3hCoUx_4MAtDGppOsErV_GIqfeu5qRoUfLCpP5gSW_k_ZTlB_oBxgtCEs8iXCXc9bEjwNg/s1600/a.png)
(x-4)(x+4)=0
x = 4 dan x = -4
Jawaban: B
8. Persamaan kuadrat
mempunyai akar-akar x1 dan x2 dengan x1 ≠ 0 dan x2 ≠ 0. Persamaan kuadrat yang akar-akarnya 1/x1 dan 1/x2 adalah ...
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiltydX7mLVO1vEcaV6AIfy3DRG7NV12J81fyM-crxttsx0AvFogc5yJO_baBJu8hGWtN6ei6lWD-7CVC8LywNjuk-OsoulmdkOhLOFU7Iw0Bh5yVLojkJxcp1I7p62YRcIcSlWpTxm5Ck/s1600/a.png)
Pembahasan:
, a = 3, b = -a, dan c = b
x1+x2=-b/a=-(-a)/3=a/3
x1.x2=c/a=b/3
PK dengan akar 1/x1 dan 1/x2 adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFt3YfehbQSLhrC1NIjAFSTJLo_eqdfLjuAWeV0j9c4xjM5FHJrCPsr28M1-2dLzCD2l2fxhJtJgO4lGsT3nnc-Tl7NDnNFmihdFeo5naxwnhTM_WAssN9-8V61Y8l_Lugtrt1YxZHYtQ/s1600/a.png)
PK yang baru adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg61CdpbIqeiy2yQ4G0jYxvZjNVzJ8_seUDcjMreqNrKHelSXSl2XdhbJbdzI20N7KHw5ekNpL44O8wCMe5yG6GQRkNByTs6JcGj9H9MEA7bR1MyN9XOjnaBvUZxsSOnfL7fiKrE82dnGo/s1600/a.png)
Jawaban: A
9. Jika selisih dua bilangan bulat positif adalah 1 dan jumlah kuadratnya adalah 4, maka jumlah dua bilangan itu sama dengan...
a. √2
b. √7
c. 3
d. √11
e. √12
Pembahasan:
Misalkan bilangan tersebut A dan B, maka:
A – B = 1
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmy8I6oKwUvf8CtqONqgcAcVbE4H25qkUX17sEDe-Du7hJbCERRBCp3WMWSXlZv_OeMsj_UVPX9Kb5QLqSWWoAd-9b1YbdV36tErj2_hmKMZw9S_IiHUnldgEumtX0FzYSeMCpkOkcE3U/s1600/a.png)
4 - 2AB=1
2AB=4-1
2AB=3
Maka:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOCvCFdN54V_462WIUVTSWfyWuOJgYkuXNbCOalIlTSWJYr4fglOsI9T4zOD3mPEhK7bN0fLE6aFJm4_NzZy8iXqIYdajXYag1DCGXlTCZ1qKkzKg9gx1Z7Ljfw1X06BSTGgDmd85Dxtw/s1600/a.png)
= 4 + 3
= 7
(A + B ) = √7
Jawaban: B
10. Akar-akar persamaan
adalah x1 dan x2. Jika x2 > x1 maka nilai 2x1 + 3x2 = ...
a. -12,5
b. -7,5
c. 12,5
d. 20
e. 22
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPuHYuNiaG41rhkCOSg1xtMtHBMBkW1SbZOKq7IoTOO4SLpkUdmO_AeffSb6ByT88Hh5yXujnHr-066TddnJfpOLFQQF7TH-mGZbr0DMa48YDv3vMx-wYvG3Lp9qGMJcv5vPRW3-gsaQQ/s1600/a.png)
(2x+1)(x-7)=0
x1=-1/2, x2=7
Maka:
2x1 + 3x2 = 2 . (-1/2) + 3 . 7
= -1 + 21
= 20
Jawaban: D
11. Jika x1 dan x2 adalah akar persamaan kuadrat
, maka persamaan kuadrat baru yang akar-akarnya x1 + x2 dan x1.x2 adalah ...
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjvc_W2EjFEwtnhmIOA9r4dIOff9Kynld_67OGpd6qgWiMzS8ORdFhz13oyXOlANiZYBeI1TnBNLBI9LDUYLceJCBnxgev34dCM5H1-qE6GXXIUSKZ_Rmx6b6CoAEvgyQB0vY2h5MQR6yg/s1600/a.png)
x1 + x2 = -b/a
x1 . x2 = c/a
PK dengan akar yang baru x1 + x2 dan x1.x2 adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQh6baZxJ2Fz4-P6QIwpl36b6qtYCecSpoKrucUDQMV1BhqHPVU70Yb3Og6Mn_fEVZXhxEYQ7BiMA_RVoX8L_h2eEZdb3L2wPxNKK4POr2ry-xEA4x3eOldcwRMhbOq1X1Yn0_TUsb_cU/s1600/a.png)
PK yang baru adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWY10Rweq2OkYSiAhN8uN72dviBscdwOpRFYt7tS3UaNDMYrYOTMRcIFKPGTK8uSl0O7bdsI9qlnXO2CXW3_MQDUCtrjLDp2NttGklNoy35WB-X6Z8QRqR5CwuvwKAUxahv1Do87XMNb4/s1600/a.png)
Jawaban: B
12. Jika akar-akar persamaan kuadrat
adalah α dan β maka nilai dari
sama dengan ...
a. 19
b. 21
c. 23
d. 24
e. 25
Pembahasan:
, a = 3, b = 5, dan c = 1
α + β = -b/a = -5/3
α . β = c/a = 1/3
maka:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhl-GulXreXl4PqkuC99ACCmhTV6zkq48rOZPex38EOFTo-X2SgJU2YM1GH6cX8vsdzNEyQoylbTuWllhBgk8P6mXm_BwVLgj28kAp7AGcIZnbYnBmtJn8LzfTAdgW1LxkXBt2Qp7AXN7k/s1600/a.png)
Jawaban: A
13. Ditentukan persamaan
dengan x ∊ R. Jumlah kuadrat akar-akarnya akan mencapai nilai minimum untuk p = ...
a. -6
b. -4
c. 4
d. 6
e. 8
Pembahasan:
, a = 1, b = p – 1, dan c = -(4 – 5p)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9A3pRyGXx9ERjnfCvAUdDZlRnJuq-gUcSuVSFSi7NOp4qWm-l6j4W74OQO4X8VJRVbhwRleq60piTx41Cg1EBLDm241NMJLgaoDEhJN3fKqnVz6vW5cRZHaiUX6n0aOei1dVedkPlP6o/s1600/a.png)
Jumlah kuadrat akar-akarnya adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrcjnCnrSOnF1Fkqhbmc_xtcPp8MLzRzyug9N96U1yxT1q2we5FP0kVTcmllx3kzGoJBQu0eixqI_koXAP9Su0R42FEL7JAi5Q9iYM21Txxp1FIibrA1Z0fOO6ty8gQW1GWO3EkDBgOgk/s1600/a.png)
Persamaan kuadrat akan mencapai nilai minimum ketika x = -b/2a
x = (-(-12))/2.1 = 6
Jawaban: D
14. Jika
maka 3/x adalah ...
a. -1
b. 1
c. 2
d. -1 atau 2
e. -1 atau -2
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5yuZUoJPgUlirBszqQ2ApUKrkocKsypVO8-3ZS9elgXydn-KcoSB9wrgRjz2G52TRBfYLQgv0nrl0IsxDyNggHrRQTu9wOtte-XpArL3q3lMJlafW80eK6wGUPgCv7kghJwhaBxdynZ0/s1600/a.png)
Maka:
3/x=3/3=1
Jawaban: B
15. Akar-akar persamaan kuadrat
adalah x1 dan x2. Nilai dari
=⋯
a. -5
b. -4
c. -1
d. 4
e. 5
Pembahasan:
, a = 3, b = 1, dan c = -2
x1+x2=-b/a=-1/3
x1.x2=c/a=-2/3
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhs3vllBPxDqkexaEXuX2iIUWeK8egCZIpbwtS14ocIWvSAb7fAMh_-O8leu3eTKFHQ4MgEr6qAmgOB5A7TYFSpyZRSvZqPnm5RcviI3VxEyyPmoY6jRzLsxlBH8jS3wslygISgZEES8Ho/s1600/a.png)
= 1 + 4
= 5
Jawaban: E
16. Akar-akar persamaan kuadrat
mempunyai beda 10. Pernyataan yang benar berikut ini adalah ...
a. Jumlah kedua akarnya 6
b. Hasil kali kedua akarnya -16
c. Jumlah kuadrat akar-akarnya 20
d. Hasil kali kebalikan akar-akarnya -1/16
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9TJ_Hp6XcO-iS9DY9p_LN57E223RLCEiai4uG-itCDjTrNoQ9gpe2G0nA9-G68MQ3Epn1RTBx3RimNH7OEMEWzMFhBKo3BgFAo2HHdJIkbGGolRjWb2_1kMHL5C1nzt4tJVU9gMm04tM/s1600/a.png)
x1- x2 = 10,maka x1=10 + x2
Pada persamaan kuadrat di atas, diketahui:
x1+x2=-b/a=-((-6))/1=6
x1 + x2 = 6, ganti x1 dengan 10 + x2
10 + x2 + x2 = 6
10 + 2x2 = 6
2x2 = 6 – 10
2x2 = -4
x2 = -4 : 2
x2 = -2
Jadi, x1 = 10 + x2 = 10 + (-2) = 8
Mari kita bahas satu persatu opsi di atas:
a. Opsi A benar, karena x1 + x2 = 8 + (-2) = 6
b. Opsi B benar, karena x1 . x2 = 8 . (-2) = -16
c. Opsi C salah, karena![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhphyINeMdTNYDx2_I2SFN7NOOJWHmWNbXyZT6RY_SKoCPAkqZ3wmu4kdKWcoAz5VYqFBos9UjYd9AtKkow4TOxZCDT4FiAVfHa2DDowJCQ9FmX_CoEhI06_ud_AQbqMQ7eOdh3V9TRa64/s1600/a.png)
d. Opsi D benar, karena 1/x1 .1/x2=1/8 .1/(-2)=1/(-16)
Jawaban: -
17. Jika p dan q adalah akar-akar persamaan
maka persamaan kuadrat yang baru yang akar-akarnya 2p + 1 dan 2q + 1 adalah ...
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjegwE3GNyZs8wK4oJV40kvTSF761lkFQoZmjH1xtM_fqdVibwTtXa5rUqLAKFmN-pCz6GNh2FtB1TFXAI35f4luKYtV6IX16ga2yTltQkr8YQUS4seUqH6vf0e7bBD0tMw-DiHTxJDHUQ/s1600/a.png)
Pembahasan:
, a = 1, b = -5, dan c = -1
p+q = -b/a = -(-5)/1 = 5
p.q = c/a = -1/1 = -1
PK dengan akar-akar 2p + 1 dan 2q + 1 adalah:
(2p + 1) + (2q + 1) = 2p + 2q + 2
= 2 (p + q) + 2
= 2 . 5 + 2
= 12
(2p + 1) (2q + 1) = 4pq + 2p + 2q + 1
= 4pq + 2 (p + q) + 1
= 4.(-1) + 2 (5) + 1
= -4 + 10 + 1
= 7
Jadi, PK yang baru adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgr_Vxb82at5124fKcSIvBwCS0o_sJxmOagLS2Hz_yfr1kU6iFQatekkJfh_0dL7m_jKdcBGiOEZPar9qPipMaaUhL8T9mFF2AHTRvgN9zWFwsAaftNd_D-XuaofPg7XYREeKMgobCXJ8g/s1600/a.png)
Jawaban: D
18. Akar-akar persamaan
adalah p dan q, p + 2q = 6 dan p ≠ 0. Nilai dari p – q = ...
a. 4
b. 2
c. -2
d. -6
e. -8
Pembahasan:
, a = 1, b = p, dan ![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-AoSd-1ibOb2BuhJTpUbsIl8UWm-OBNLoMs2KtFInC6NV6Rj71lLnkDSLGv_dmquCU23SSq_eMnTXp2N7EKfWTsV09K4VS7VEl7NsAkj8EuE93BmFw6jZIuGM1RD3NoFKyKC8e3zc6Po/s1600/a.png)
p + q = -b/a = -p/1 = -p
p + 2q = 6
p + q + q = 6
(p + q) + q = 6
-p + q = 6
-(p – q) = 6
p – q = -6
Jawaban: D
19. Akar-akar persamaan kuadrat
adalah α dan β. Persamaan kuadrat baru yang akar-akarnya (α + 2) dan (β + 2) adalah ...
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNsK9x-odiZsV4bGSjUoRGw5vOu44Qy5AOe3vX5ksaJVknXOcbDpxZFubiIscs_GrzLRw_pbivA8EFzSMQp_XooAx5oldXa_AoI5Ok64eHsMmMK2JZgT0KVnpu54Ex-O9kXEh1P_gITJw/s1600/a.png)
Pembahasan:
, a = 3, b = -12, dan c = 2
Persamaan kuadrat di atas memiliki akar α dan β, maka:
α + β = -b/a = -(-12)/3 = 4
α . β = c/a = 2/3
akar-akar baru adalah (α + 2) dan (β + 2), maka:
(α + 2) + (β + 2) = α + β + 4
= 4 + 4
= 8
(α + 2) . (β + 2) = α . β + 2α + 2β + 4
= α . β + 2(α + β) + 4
= 2/3 + 2.4 + 4
= 2/3 + 8 + 4
= 2/3 + 12
= 2/3 + 36/3
= 38/3
Maka, persamaan kuadrat yang baru adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLzRPrNtNBDkeP_YpwWTxB-dYyjdoLB08VLp7XLr2sMH6BFcRvUS3w-miCz33RXJxdqvo9X7vmR7x1BhmMM_iuDvgO1sM6jjxY5WMGKpDIFE-zZ-Af-Z2qw0mtGZ4U3Ndp6yZuQYvFrik/s1600/a.png)
Jawaban: A
20. Akar-akar persamaan
adalah p dan q. Jika p = 2q, untuk p > 0 dan q < 0. Nilai a – 1 = ...
a. -5
b. -4
c. 2
d. 3
e. 4
Pembahasan:
, a = 1,b = 2a - 3 , dan c = 18
Persamaan kuadrat tersebut memiliki akar p dan q, dimana p > 0 dan q < 0, maka:
p + q = -b/a = -(2a - 3)/1 = -2a + 3
p . q = c/a = 18/1 = 18
karena p =2q maka:
p . q = 18
2q . q = 18
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja-c0alHLEfdJWU1v_lL8FFSsCecPoMq6S7yLNb6S1w6vo4IXxn9OlWB1Twaz237Jx8tipsg7llvcpZJ1z7g66RYy_zDi6Y-hn_PVjNDI_GSQYU0z77t9TF68nfYVCgM9i-rPiOoZv_Dw/s1600/a.png)
q = √9
q = 3
Karena p = 2q, maka p = 2 . 3 = 6
Nilai a adalah:
p + q = -2a + 3
6 + 3 = -2a + 3
9 = -2a + 3
2a = 3 – 9
2a = -6
a = -6/2
a = -3
nilai dari a – 1 = -3 – 1 = -4
jawaban: B
21. Akar-akar persamaan
adalah α dan β. Nilai minimum dari
dicapai untuk a = ...
a. -7
b. -2
c. 2
d. 3
e. 7
Pembahasan:
, a = 1, b = -a – 3 , dan c = 4a
Persamaan kuadrat di atas memiliki faktor α dan β, maka:
α + β = -b/a = -(-a – 3)/1 = a + 3
α . β = c/a = 4a/1 = 4a
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiopO4a15P57u2YEjs-aEPi9iue2DX00ybD31iqtZ8NkJalTPzXEqFr8kNQhOrr5qwOxOnzjg4pUiggPYQtX-FNdVvdwW5Fj_4bI3868D-6vQHZg2O4o_Nrr5c4MYUKfNAHDgrgR3f1vAc/s1600/a.png)
Mencapai nilai minimum ketika a = -b/2a = -14/2.1 = -7
Jawaban: A
22. Garis y = 2x + k memotong parabola
dititik (x1,y1) dan (x2,y2). Jika
maka nilai k = ...
a. -1
b. 0
c. 1
d. 2
e. 3
Pembahasan:
Karena Garis y = 2x + k memotong parabola
maka:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRoJJbnziy_0u68HmBXoVXhGkjoUjpyAsgsDW7e7I3GWE0thuctocaUXdAJLpKsvnmcGdO9jq6h2exvNx8kRSaRVI0Zw_s0lYeUA_zaxXd_hdD115sx90_UMI_2TyL4T3UZ46tdOcncEc/s1600/a.png)
Karena berpotongan di (x1,y1) dan (x2,y2), maka akar-akar dari persamaan kuadrat tersebut adalah x1 dan x2, maka:
x1 + x2 = -b/a = -(-3)/1 = 3
x1 . x2 = c/a = 3 - k/1 = 3 – k
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhsXJ5QNWW5DcFYvNyn0PiQSorEZYmaMIbQtjqZQdpcYabsExkQKeJkrass_fbI8n_q5G0qtexGSFZWDkfkHizu2II1C7Pt1BD9kO5yu8U2UbIQlqm8jtu38hqOW27yCfe-WPxmNbPqf9k/s1600/a.png)
= 9 – 6 + 2k = 7
= 3 + 2k = 7
= 2k = 7 – 3
= 2k = 4
= k = 4/2
= k = 2
Jawaban: D
23. Kedua persamaan
dan
mempunyai akar-akar real untuk ...
a. -1/2 ≤ k ≤ 2
b. -1/4 ≤ k ≤ 1
c. -1/8 ≤ k ≤ 1
d. -1/8 ≤ k ≤ 2
e. -1/8 ≤ k ≤ 1
Pembahasan:
Persamaan kuadrat memiliki akar-akar real jika memenuhi D ≥ 0, maka:
Untuk persamaan![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvMlVjxnikph_DbuHIbJUXzfmUT9E7TzZxK2pitPjuzQvCgvA7b8OlXR_aTvDt0iSQyQia9SwSLyTSIrIA_P6vJUz97-Cn8WzXetPqpKkdAJpCiDsX53bIseotqSLtCR9_EhsGKQlQ3yo/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgC9oHML0tic6ioHoss8lF7hnA_LeuLAEteyDoY6lzALC9oTuxbNJqYsZB54UUX136Kf0Fx3NHnKJiWWRdemEQAlItM64K2Kt1Vam9PbwiroWRKxPnYAvfGEpAmKIauBh1bC2OKPCgNdDY/s1600/a.png)
4 – 4k ≥ 0
-4k ≥ -4
k ≤ -4/-4
k ≤ 1
untuk persamaan![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1yLXhq0eEQF0YwcnhysP6f3RbRQ8W6LyXTHQV4R1KDJqSn_F4OaKNAkM99hX7RDtludQH7N91EbS00wCxo6Jax5p2Eb8cv8xd07ZYwqWAnuM67FbxW8OpHwsMLmQGAaPLBsY6u3h_q14/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNMDpPixPBMy_4XUuonRYb0ExVIoRRT2psJcSK5Ohyphenhypheng8fg88pOuimGzw0JLD5FHwTDuzHsTsKkokhE1kZ4M3y6xouUmx2FTV6FY-UOxxA4IsOE819stRfjbb8EsNJv0a9501CITIPHczc/s1600/a.png)
1 + 8k ≥ 0
8k ≥ -1
k ≥ -1/8
jadi, nilai k yang memenuhi adalah -1/8 ≤ k ≤ 1
jawaban: C
24. Himpunan penyelesaian persamaan:
adalah ...
a. Φ
b. {0}
c. {-2}
d. {0, -2}
e. {0, 2}
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtW4gweJXkAsZZjkpu_gcFKXUF26CT7Biv7R5LNv3suTMZEhV7de3n3ruja3_hOGVXV50KsoNdXzrjpjKuSRFsbbP3UhRgXe4bX96iTtd58_FFvyVe4F1Y4QsONygVMQUwmJSknr6Kkck/s1600/a.png)
x (x+2)=0
x = 0 atau x = -2
jawaban: D
25. Diberikan persamaan kuadrat
. Satu akarnya merupakan kelipatan 4 dari akar yang lain. Maka a, b, dan c memenuhi hubungan...
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEht4A2H0v3LSypXuF21Bdskts7j9H43Xv7Hsm7vC80SGV97H8hjyRjIxa0C2sRQt0pGmNkPI2YN8mOHM3agQd7SoRMMeuQdxi-Q3gYRXbe-z1qvskLOSVP7EMUyHHuOB2DwhGNXuphVUSk/s1600/a.png)
Pembahasan:
, misalkan memiliki akar-akar p dan q. Pada soal diketahui p =4q
Maka:
p + q = -b/a
4q + q = -b/a
5q = -b/a
q = -b/5a
p . q = c/a
4q . q = c/a
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5TpGo-FL9YQXjvxlA1r2d09OOJYg26HKaduWgGSvwAI8ITbMGEKLFBsLVQqkkbyO6Rjt3GOw5obV1BvQEXZXSKOQaTiJSIBdBmZqMkFWbg5OgVqvz3ENhEjP2aa_8sIx_GH0LBETenBM/s1600/a.png)
Jawaban: E
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8Wjhw1Dya6-zPhFc7SSp5ASEsqPdFVnow7wSnlnBNXiUhX6hq122PNA_-hY9Cp1u5EKdz6AB7CYRImUHwpawzTumA1rv4-VNYs7rIY99oXaqzW93KSZSe_E3cpgsoArSjAMGxd-D7PqM/s1600/a.png)
a. -8
b. -6
c. 4
d. 6
e. 8
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggSjJPJ2GTs0d690jOYKH_etGwJvV6ewS__aE9d6K03Z9T51bpsAw9BWf77NIfO2Zq7D0mVKbT2AYP_z_ch6P_WqIah0qjlNbYl5Sd86KDbmvKMq5RCF59hzvddHL1quqp8AN6ZlbCfrM/s1600/a.png)
Pada soal diketahui PK:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8Wjhw1Dya6-zPhFc7SSp5ASEsqPdFVnow7wSnlnBNXiUhX6hq122PNA_-hY9Cp1u5EKdz6AB7CYRImUHwpawzTumA1rv4-VNYs7rIY99oXaqzW93KSZSe_E3cpgsoArSjAMGxd-D7PqM/s1600/a.png)
x1 – x2 = 5, maka:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdaqljK-eVj07ju-uvaq4xDXVJbRBf4PIsRo2V3FaH7Sf0APX1hIv-2-LMLQ5VLOz9vQWwvQz2s4hArR-Vx_EtypmSx-vSEw1Ym42ydD7dtdjZRrVYmWemNZOL89_8nyz2LeMZEgBtOXc/s320/a.png)
100=36+8p
100 – 36 = 8p
8p = 64
P = 64 : 8
P = 8
Jawaban: E
2. Akar-akar persamaan kuadrat
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgasoH8DBo-_9bZKayKjcQTBNhU26GeLieRtOYNnlcYsZo7tpDqjPw-FDZmYIFiuZ6A6Q3_Y4zz-SixbxnO8gjAjncqi_ThlmknKsMbAiwGNiJ16VBGF6H__CX5odyQ5S2JduG3PSxGcLc/s1600/a.png)
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgasoH8DBo-_9bZKayKjcQTBNhU26GeLieRtOYNnlcYsZo7tpDqjPw-FDZmYIFiuZ6A6Q3_Y4zz-SixbxnO8gjAjncqi_ThlmknKsMbAiwGNiJ16VBGF6H__CX5odyQ5S2JduG3PSxGcLc/s1600/a.png)
Akar-akar PK di atas adalah α dan β, maka:
α + β = -b/a = -2/1 = -2
α . β = c/a = 3/1 = 3
persamaan kuadrat baru dengan akar (α – 2) dan (β – 2) adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZLH1JJ0OMkQ5mJpVUd5QZ39F13fD4Y-HdJzv05Yfjf9oNf07kaRNoE0UKCRHxuZoA1T8qK89R2AVtnymi3AgWJ9EYcXLt8sw59RwBwf4fQ-J1GxJmNC_O7uQUGVP75QmCfwODDXyWPFA/s320/a.png)
Jawaban: C
3. Jika a dan b adalah akar-akar persamaan
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZQWbI6WNVvJqTnMBsnyd_d1M4S69X-wWxgkY-qqySykWEQjW_cYs9B5_6izp1Xd74Zw8i5TQ7W_gz_1cB3LwDvVYISbV4RP_hAgrvrEORVPXY4Orcm7LoOZS6thzjzerIb1pMQxNxwhQ/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4bkaIaGyXDCUpThB8XxP8Uw36YilQkbAJyED6FceH0KfEUHo6OwX83nsly-2-RN_4uAFCvGSTNvzwyO_ayX0XjxrtxTDXaOdtJnf4bVOJaitJhYlglbzljN77ktDSEUABJIkBiOBnSGc/s1600/a.png)
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZQWbI6WNVvJqTnMBsnyd_d1M4S69X-wWxgkY-qqySykWEQjW_cYs9B5_6izp1Xd74Zw8i5TQ7W_gz_1cB3LwDvVYISbV4RP_hAgrvrEORVPXY4Orcm7LoOZS6thzjzerIb1pMQxNxwhQ/s1600/a.png)
Akar-akar persamaan PK di atas adalah a dan b, maka:
a + b = -b/a = -(-3)/2 = 3/2
a . b = c/a = -5/2
persamaan kuadrat baru yang akar-akarnya -1/a dan -1/b adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgk72YRXnRJ34IPgih1tHHjg0TaUneA25A7WRmQFHUY7JKInPDfzI9FzAYQAP5RM75yAP5zeF8oU2Z3Yra6Wqmty4pIWVjmywWzvrePd_Aa9DCZAMkq4yE1zIPozAY7gns1hGw1LH-jZQk/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7JXKw_-gnNWUAw_7lqkK2j2U_cflVPSOKbI_THYlFzJyd2x_O9J4ZbzWWArYV1iIy7vjRA0GMVv8L548KpU3OU3qk29jFA85mMy8tuTqVAwxGRlfK5b1Ql6vDkIUxLgD7GVd1ZG-OxyQ/s1600/a.png)
Jawaban: D
4. Persamaan
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDsKBaofY0V5c2gnHG_emGcVLC8_j3buf5gxhWuL_SbYVz-lf6JsQN8IVV_0l-WY09b3gwHLoWhE3dADeEcoCRKe8tpyQi9uf_r0ecHhYdR-uRoL4nOSvypsOJML3yg2ZW5SFTQnR8QWw/s1600/a.png)
a. -3 atau 1
b. -1 atau 3
c. 1 atau 3
d. 1 atau -2
e. -2 atau 3
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDsKBaofY0V5c2gnHG_emGcVLC8_j3buf5gxhWuL_SbYVz-lf6JsQN8IVV_0l-WY09b3gwHLoWhE3dADeEcoCRKe8tpyQi9uf_r0ecHhYdR-uRoL4nOSvypsOJML3yg2ZW5SFTQnR8QWw/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_Es_CBYPImz5OFn7EKT856uywUl2ouDjOv4HYdORtlxhFuMarY5EER2QxGIgWCwhKX7s7jAOlaruExEZjQWt00TcCOs94B3brSO7eWXIpUrIlIeATzAYSepq9_b1NXBTnA5Lbj3ci1Ic/s1600/a.png)
Syarat sebuah persamaan memiliki akar real sama adalah D = 0
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTHx-EQYXFmSppXBRvyx5eiUlQUrveUBzK_h226AOJh5gHR4H5GNfJXrlGMMad-fc_W0_TbhP6KOABHDt4Kuxnh-mPeaeHuF_CmOUfsCNjO-EQA50Fkq4VGmKZ_13oOQbqChW3H_s6v8E/s1600/a.png)
(p-3)(p+1)=0
p = 3 atau p = -1
Jawaban: B
5. Jika x1 dan x2 akar-akar persamaan kuadrat
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjghVpRGjKGMvf3iNQQxIqYeLASVNzLNJKs8XJdFOQzjIFHtP9f6135xtxyUplX32zB2SsSz3KId-3BRgpBYk_drvOwKcgrQ8lXNe18iwFKWuc64HCK4MQhkJG9WNyGTkwr7xDjMaLHa7Q/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg361zuXPobHJCNN6HDU1i2_gmdgoRWRiH25ncBLPfovoZMWrCCHXUjhSWNxgIIWBgKaYirUPhg8jgc8n8BpQhYFDeb8E7dIJRTMo0Hl_3f4elp2UMECqwGTrvRpME8eS_bDnQc3loYPhQ/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7aYvfDrCPanN5yX3hMIo-mdd_ek4SVCuIXdYKjbHzxeXgfk-N35K-BLr9dUxVUq4nriQYCv-EX_yWxxDI3KdPrGLoiSN9GTWeWWSdHO8oYdWDmK8dLGs_aX3WonFUFm5jzztqyVut-0M/s1600/a.png)
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjghVpRGjKGMvf3iNQQxIqYeLASVNzLNJKs8XJdFOQzjIFHtP9f6135xtxyUplX32zB2SsSz3KId-3BRgpBYk_drvOwKcgrQ8lXNe18iwFKWuc64HCK4MQhkJG9WNyGTkwr7xDjMaLHa7Q/s1600/a.png)
PK di atas memiliki akar-akar x1 dan x2, maka:
x1 + x2 = -b/a = -1/2
x1. x2 = c/a = -2/2 = -1
PK baru dengan akar
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg361zuXPobHJCNN6HDU1i2_gmdgoRWRiH25ncBLPfovoZMWrCCHXUjhSWNxgIIWBgKaYirUPhg8jgc8n8BpQhYFDeb8E7dIJRTMo0Hl_3f4elp2UMECqwGTrvRpME8eS_bDnQc3loYPhQ/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEii1qmp5BKraopFK0Um3latTuRhyphenhyphenFenh4NwrX1f7ZrUWRJ0GcJfklFQICcD3QHXuMnfW3Y24dDjjejkHOb8B-084ocTURv44ANUKYd4XQ3hDRXrGCPJu_KbJ-yFVs2orQxjf4iY9fxYXPE/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUxMjx8KPz6wVWsxC6p5xq3rEWLc8JToEzR4dcmN0YdlpF0h2cB59z7bsWORXqtYrXEr8Kaoy72KBk2AEOPddiVd_lKltkq4xNj393RGTP4haoW-utfmKOARhdAqL9kLBUZnEIKvwl_B4/s1600/a.png)
Maka, PK yang baru:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0dXncqprdhH4QNPDbLX5l88EBPAlvhJb6TFOgG88FCa-dHMuNuRrdaB6U1wyxpb8DNGYBPfkbZjcjzdZuJUdbbhLzjPrzY3YUwgECLGSyCkt8D7Nu5LC6i88TyuXZjWywCAI6c0cj9p4/s1600/a.png)
Jawaban: B
6. Akar-akar persamaan kuadrat
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEintrOFWENvbIFs_xOx1goLCZ-fNnfcsHtjZhNQSe48u-KW235s3MHEuBAfOtwRom_iMCjgTSvm4UhUIP8-oF3jab8shPGXlsOn7q4OZY0g3_H170kJl2cZvOfsjQJYIWAeScgAKzpZ0o8/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZfxN3sxK_ZndAhiBbWZ4FXvqlb8D-83QLJyHTJh1zhCKTgqLKQtL_Q_KQG8QWN_5EIiZ6RISmVWZ0FvS3ysDF2BarMb3fXseRKV5tZeHtX7iIRh4EvkJhjv8HmslwgwqhD8fvNvqc7yA/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhB84teIz-Ob70SbZsHU4nCLlpb9vdQgUDCrPvbKsrw_c8HmgqTq_IBspdQ-PqbsUJyJwiSBWwx-2VvlH9Y7nYJWlqXGjZpSFkLhSLoI9WkJTZ6EPVtwCPQfndKPm5Nj7fcxdcRZgWFwWE/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkZ7qpNP0S-YwtHhRhxVAs80uSnDbHMj91fQcvyPnyF-FcWc9k_Mwk-_azRR7IUqNlu1frJuSPlyk86EC9AcLN37fgUMzC7bTzVsI6tPCOzm9HQa5DM4hJCqWifFmJwD-_MgMRvDdmCZE/s1600/a.png)
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEintrOFWENvbIFs_xOx1goLCZ-fNnfcsHtjZhNQSe48u-KW235s3MHEuBAfOtwRom_iMCjgTSvm4UhUIP8-oF3jab8shPGXlsOn7q4OZY0g3_H170kJl2cZvOfsjQJYIWAeScgAKzpZ0o8/s1600/a.png)
PK di atas memiliki akar
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZfxN3sxK_ZndAhiBbWZ4FXvqlb8D-83QLJyHTJh1zhCKTgqLKQtL_Q_KQG8QWN_5EIiZ6RISmVWZ0FvS3ysDF2BarMb3fXseRKV5tZeHtX7iIRh4EvkJhjv8HmslwgwqhD8fvNvqc7yA/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-Tpef-t-nFrub-6WKtDf3Ska1STXTOISpxfkxZTyINPWTxnl05dRynIW9GmSMsfr6voBZk-BCX-5uag1MSPVG8-h9_ftSMYkHI7HkcXhOhe7CuWZj7oD4J3SVJYRjoTiIzF_GB9Gwl1w/s1600/a.png)
PK baru dengan akar
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhB84teIz-Ob70SbZsHU4nCLlpb9vdQgUDCrPvbKsrw_c8HmgqTq_IBspdQ-PqbsUJyJwiSBWwx-2VvlH9Y7nYJWlqXGjZpSFkLhSLoI9WkJTZ6EPVtwCPQfndKPm5Nj7fcxdcRZgWFwWE/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8-fKOB11ox1WIwKIklPNcPZkjwQMM_uS6x4lBQ099_SWoeEGWYyO7PsvUoLoj9QkjezZy9yh_HTT_3ijDUSylsedPafVJDR9w9cjB-qpKvMdptt7dgBClhfxzbNgDpYAN8X-v7iDX5Bc/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHTLToIUSx9vqx6KALPmzVX-NV6Jm8NCYshFgi6mSwXY3mKsfdIHBlwb9QTkOJ_Ovsic_LwEN4-lSybQHrxhO442eZV5mBSYj425-o6QBjSkuRSNWSs8Om4vO36KO0bCjr8HYzKYzuU7E/s1600/a.png)
PK yang baru adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTvRHs4DD9GhznkYGuK3pYo1JAHqERhWIomhFQS5OwrHPXD-Oj54CBCTJAyDIMBzcMZs8GEXK5MEWlx_aaoNIUphV12Q7XKLXvjYZ_Mb-umFgpi7gJuHLUHrszD3EHMozSerDX42AC8Us/s1600/a.png)
Jawaban: E
7. Jika jumlah kedua akar persamaan kuadrat
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJ0_2Qo81fyACjD7dGMxZEfsL_gt9YDI_0eYZuT_HuGx8dULyP66K3wat2SJfMp7sKu8BXUomHFEL4OzQVjRwcTayyk7YXhFp4oIkupD_ldtP65Z_0sxVehqlie8wSAjmYxURZcx9yF8E/s1600/a.png)
a. 3/2 dan -3/2
b. 4 dan -4
c. 5/2 dan -5/2
d. 5 dan -5
e. 3 dan -3
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJ0_2Qo81fyACjD7dGMxZEfsL_gt9YDI_0eYZuT_HuGx8dULyP66K3wat2SJfMp7sKu8BXUomHFEL4OzQVjRwcTayyk7YXhFp4oIkupD_ldtP65Z_0sxVehqlie8wSAjmYxURZcx9yF8E/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDU1jx3TRAxGNnq9HuvcyHUl1rba6I5N-5aUjVntcWzdBW-baQH_LnvbOGO7fsXiLch_byZ0N9VHqkH1M6LxzACbCzmpavXh64lZ-_7FaAjvHEU9c3xlWfsLAXLSL3MRVpMxcSWn8le2U/s1600/a.png)
x1 + x2 = 0
-b/a = 0
-(2p – 3)/1 =0
-2p + 3 = 0
2p = 3
p = 3/2
Maka PK di atas menjadi:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiKR6Dk6Uhqv-kTOfIX4LUnzQD_laxQKnM7xIbBTbK_3-i0zAi0wUXM8pY884AhxqF0ES3f3hCoUx_4MAtDGppOsErV_GIqfeu5qRoUfLCpP5gSW_k_ZTlB_oBxgtCEs8iXCXc9bEjwNg/s1600/a.png)
(x-4)(x+4)=0
x = 4 dan x = -4
Jawaban: B
8. Persamaan kuadrat
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiT_S7psJExR6apkSbFxr6vRLYr09-bzIhE4NyWKTg6CyOgt848130J6pxdVfbVkY5EoQ-lm_G5KZc2sQzw1D3VeGqtC-5BivmkSxRZWEF5MaNYAiqnWHkotGGeFqJYcSL2s-hLOY9DL8s/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiltydX7mLVO1vEcaV6AIfy3DRG7NV12J81fyM-crxttsx0AvFogc5yJO_baBJu8hGWtN6ei6lWD-7CVC8LywNjuk-OsoulmdkOhLOFU7Iw0Bh5yVLojkJxcp1I7p62YRcIcSlWpTxm5Ck/s1600/a.png)
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiT_S7psJExR6apkSbFxr6vRLYr09-bzIhE4NyWKTg6CyOgt848130J6pxdVfbVkY5EoQ-lm_G5KZc2sQzw1D3VeGqtC-5BivmkSxRZWEF5MaNYAiqnWHkotGGeFqJYcSL2s-hLOY9DL8s/s1600/a.png)
x1+x2=-b/a=-(-a)/3=a/3
x1.x2=c/a=b/3
PK dengan akar 1/x1 dan 1/x2 adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFt3YfehbQSLhrC1NIjAFSTJLo_eqdfLjuAWeV0j9c4xjM5FHJrCPsr28M1-2dLzCD2l2fxhJtJgO4lGsT3nnc-Tl7NDnNFmihdFeo5naxwnhTM_WAssN9-8V61Y8l_Lugtrt1YxZHYtQ/s1600/a.png)
PK yang baru adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg61CdpbIqeiy2yQ4G0jYxvZjNVzJ8_seUDcjMreqNrKHelSXSl2XdhbJbdzI20N7KHw5ekNpL44O8wCMe5yG6GQRkNByTs6JcGj9H9MEA7bR1MyN9XOjnaBvUZxsSOnfL7fiKrE82dnGo/s1600/a.png)
Jawaban: A
9. Jika selisih dua bilangan bulat positif adalah 1 dan jumlah kuadratnya adalah 4, maka jumlah dua bilangan itu sama dengan...
a. √2
b. √7
c. 3
d. √11
e. √12
Pembahasan:
Misalkan bilangan tersebut A dan B, maka:
A – B = 1
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmy8I6oKwUvf8CtqONqgcAcVbE4H25qkUX17sEDe-Du7hJbCERRBCp3WMWSXlZv_OeMsj_UVPX9Kb5QLqSWWoAd-9b1YbdV36tErj2_hmKMZw9S_IiHUnldgEumtX0FzYSeMCpkOkcE3U/s1600/a.png)
4 - 2AB=1
2AB=4-1
2AB=3
Maka:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOCvCFdN54V_462WIUVTSWfyWuOJgYkuXNbCOalIlTSWJYr4fglOsI9T4zOD3mPEhK7bN0fLE6aFJm4_NzZy8iXqIYdajXYag1DCGXlTCZ1qKkzKg9gx1Z7Ljfw1X06BSTGgDmd85Dxtw/s1600/a.png)
= 4 + 3
= 7
(A + B ) = √7
Jawaban: B
10. Akar-akar persamaan
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPuHYuNiaG41rhkCOSg1xtMtHBMBkW1SbZOKq7IoTOO4SLpkUdmO_AeffSb6ByT88Hh5yXujnHr-066TddnJfpOLFQQF7TH-mGZbr0DMa48YDv3vMx-wYvG3Lp9qGMJcv5vPRW3-gsaQQ/s1600/a.png)
a. -12,5
b. -7,5
c. 12,5
d. 20
e. 22
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPuHYuNiaG41rhkCOSg1xtMtHBMBkW1SbZOKq7IoTOO4SLpkUdmO_AeffSb6ByT88Hh5yXujnHr-066TddnJfpOLFQQF7TH-mGZbr0DMa48YDv3vMx-wYvG3Lp9qGMJcv5vPRW3-gsaQQ/s1600/a.png)
(2x+1)(x-7)=0
x1=-1/2, x2=7
Maka:
2x1 + 3x2 = 2 . (-1/2) + 3 . 7
= -1 + 21
= 20
Jawaban: D
11. Jika x1 dan x2 adalah akar persamaan kuadrat
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjvc_W2EjFEwtnhmIOA9r4dIOff9Kynld_67OGpd6qgWiMzS8ORdFhz13oyXOlANiZYBeI1TnBNLBI9LDUYLceJCBnxgev34dCM5H1-qE6GXXIUSKZ_Rmx6b6CoAEvgyQB0vY2h5MQR6yg/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTqtwdpxd6W1xXiVsScAhOvX7gn7y1BAF_POWVbAWOrbgAwdu0L9nU6boIb7RBa4qpuyn4j1uf33wZ7Y5_Rtdth2Sf4niXhXj7ptu-2o8Q93hPJhNn4Bvrlzr5x18R1AvO3JwVzYeLqHw/s1600/a.png)
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjvc_W2EjFEwtnhmIOA9r4dIOff9Kynld_67OGpd6qgWiMzS8ORdFhz13oyXOlANiZYBeI1TnBNLBI9LDUYLceJCBnxgev34dCM5H1-qE6GXXIUSKZ_Rmx6b6CoAEvgyQB0vY2h5MQR6yg/s1600/a.png)
x1 + x2 = -b/a
x1 . x2 = c/a
PK dengan akar yang baru x1 + x2 dan x1.x2 adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQh6baZxJ2Fz4-P6QIwpl36b6qtYCecSpoKrucUDQMV1BhqHPVU70Yb3Og6Mn_fEVZXhxEYQ7BiMA_RVoX8L_h2eEZdb3L2wPxNKK4POr2ry-xEA4x3eOldcwRMhbOq1X1Yn0_TUsb_cU/s1600/a.png)
PK yang baru adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWY10Rweq2OkYSiAhN8uN72dviBscdwOpRFYt7tS3UaNDMYrYOTMRcIFKPGTK8uSl0O7bdsI9qlnXO2CXW3_MQDUCtrjLDp2NttGklNoy35WB-X6Z8QRqR5CwuvwKAUxahv1Do87XMNb4/s1600/a.png)
Jawaban: B
12. Jika akar-akar persamaan kuadrat
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinbjFP2b1P6SkMlBEnpohwD83n1_owfcyR9koLvgOIhW3FK5A6ZdUKEmeZLqX3bRAbdj_wDvwrsTBrLbDJQ0obAj0C4McGF3TvgIaMjxDqSfDoRfr9fU2o4JQwxJ4zDT1TuYYA6HXhbOE/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2NisONl-DI3Z4nc5g-laO_9Urz12ewCS3UtGTecPZGZMLV8q79_ljDgZLxaD025pGDNBfD3Hq7L1f77PB6x7NqKfN5SZpeqHZmQKBcNrzyEyUHYGcmZ5yMYG0vP1nltTAxUAkH6OWMQE/s1600/a.png)
a. 19
b. 21
c. 23
d. 24
e. 25
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinbjFP2b1P6SkMlBEnpohwD83n1_owfcyR9koLvgOIhW3FK5A6ZdUKEmeZLqX3bRAbdj_wDvwrsTBrLbDJQ0obAj0C4McGF3TvgIaMjxDqSfDoRfr9fU2o4JQwxJ4zDT1TuYYA6HXhbOE/s1600/a.png)
α + β = -b/a = -5/3
α . β = c/a = 1/3
maka:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhl-GulXreXl4PqkuC99ACCmhTV6zkq48rOZPex38EOFTo-X2SgJU2YM1GH6cX8vsdzNEyQoylbTuWllhBgk8P6mXm_BwVLgj28kAp7AGcIZnbYnBmtJn8LzfTAdgW1LxkXBt2Qp7AXN7k/s1600/a.png)
Jawaban: A
13. Ditentukan persamaan
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpDqEDlo8JiNELC7LS_pejF8UjQfrL7rAUo9SBVzpLv6r6Xa0-qmL42zJ7vK45kQV0nZnzouKwmEAzD8YZLKi6pRfvL-hHnn22hLQGeAFj0cQ6GEENIquIgzG5wwDUf2IEUx3SiC5QgSo/s1600/a.png)
a. -6
b. -4
c. 4
d. 6
e. 8
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpDqEDlo8JiNELC7LS_pejF8UjQfrL7rAUo9SBVzpLv6r6Xa0-qmL42zJ7vK45kQV0nZnzouKwmEAzD8YZLKi6pRfvL-hHnn22hLQGeAFj0cQ6GEENIquIgzG5wwDUf2IEUx3SiC5QgSo/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9A3pRyGXx9ERjnfCvAUdDZlRnJuq-gUcSuVSFSi7NOp4qWm-l6j4W74OQO4X8VJRVbhwRleq60piTx41Cg1EBLDm241NMJLgaoDEhJN3fKqnVz6vW5cRZHaiUX6n0aOei1dVedkPlP6o/s1600/a.png)
Jumlah kuadrat akar-akarnya adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrcjnCnrSOnF1Fkqhbmc_xtcPp8MLzRzyug9N96U1yxT1q2we5FP0kVTcmllx3kzGoJBQu0eixqI_koXAP9Su0R42FEL7JAi5Q9iYM21Txxp1FIibrA1Z0fOO6ty8gQW1GWO3EkDBgOgk/s1600/a.png)
Persamaan kuadrat akan mencapai nilai minimum ketika x = -b/2a
x = (-(-12))/2.1 = 6
Jawaban: D
14. Jika
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdtGbGm-A5ASOmxaS3MiYb8m6TPzs9YSnEPMeZFTaRbVrfPxdzWwhtVpu6UUQjCq5SmybtSK2L2b9D8sZOPRC6wQODVcV6akwE9YoJ2Gv1D3OSpRRc-Z3tdQYOW__itVDblIGj5nKtr4k/s1600/a.png)
a. -1
b. 1
c. 2
d. -1 atau 2
e. -1 atau -2
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5yuZUoJPgUlirBszqQ2ApUKrkocKsypVO8-3ZS9elgXydn-KcoSB9wrgRjz2G52TRBfYLQgv0nrl0IsxDyNggHrRQTu9wOtte-XpArL3q3lMJlafW80eK6wGUPgCv7kghJwhaBxdynZ0/s1600/a.png)
Maka:
3/x=3/3=1
Jawaban: B
15. Akar-akar persamaan kuadrat
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhv8Am3GikhqTInqMYo1CcOClR6JImskiI4iDkMg8i8FejRtRXoZ_E-_2oHpFbmAs8mWHPHmfahpUzMbnxDK5hZlJbQ6Fz1ww6V7Y-wjRIYO0BZxf1c5Ar2N5agH_0kLGaEtgaGdY9J2YU/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0rE7cI-UVYN-3F4_9760tYVqiQUdMVr422oHItvN1l4HILQZUB1Z2VYG5fnU93ChkEte3w9tiz3pLgWWTvjaOBKNxAFdHz9Z2KpKXkC7TlS2W2Yg4SDlXmt_MG_OeIRLNYrsLxKE_9f4/s1600/a.png)
a. -5
b. -4
c. -1
d. 4
e. 5
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhv8Am3GikhqTInqMYo1CcOClR6JImskiI4iDkMg8i8FejRtRXoZ_E-_2oHpFbmAs8mWHPHmfahpUzMbnxDK5hZlJbQ6Fz1ww6V7Y-wjRIYO0BZxf1c5Ar2N5agH_0kLGaEtgaGdY9J2YU/s1600/a.png)
x1+x2=-b/a=-1/3
x1.x2=c/a=-2/3
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhs3vllBPxDqkexaEXuX2iIUWeK8egCZIpbwtS14ocIWvSAb7fAMh_-O8leu3eTKFHQ4MgEr6qAmgOB5A7TYFSpyZRSvZqPnm5RcviI3VxEyyPmoY6jRzLsxlBH8jS3wslygISgZEES8Ho/s1600/a.png)
= 1 + 4
= 5
Jawaban: E
16. Akar-akar persamaan kuadrat
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9TJ_Hp6XcO-iS9DY9p_LN57E223RLCEiai4uG-itCDjTrNoQ9gpe2G0nA9-G68MQ3Epn1RTBx3RimNH7OEMEWzMFhBKo3BgFAo2HHdJIkbGGolRjWb2_1kMHL5C1nzt4tJVU9gMm04tM/s1600/a.png)
a. Jumlah kedua akarnya 6
b. Hasil kali kedua akarnya -16
c. Jumlah kuadrat akar-akarnya 20
d. Hasil kali kebalikan akar-akarnya -1/16
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9TJ_Hp6XcO-iS9DY9p_LN57E223RLCEiai4uG-itCDjTrNoQ9gpe2G0nA9-G68MQ3Epn1RTBx3RimNH7OEMEWzMFhBKo3BgFAo2HHdJIkbGGolRjWb2_1kMHL5C1nzt4tJVU9gMm04tM/s1600/a.png)
x1- x2 = 10,maka x1=10 + x2
Pada persamaan kuadrat di atas, diketahui:
x1+x2=-b/a=-((-6))/1=6
x1 + x2 = 6, ganti x1 dengan 10 + x2
10 + x2 + x2 = 6
10 + 2x2 = 6
2x2 = 6 – 10
2x2 = -4
x2 = -4 : 2
x2 = -2
Jadi, x1 = 10 + x2 = 10 + (-2) = 8
Mari kita bahas satu persatu opsi di atas:
a. Opsi A benar, karena x1 + x2 = 8 + (-2) = 6
b. Opsi B benar, karena x1 . x2 = 8 . (-2) = -16
c. Opsi C salah, karena
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhphyINeMdTNYDx2_I2SFN7NOOJWHmWNbXyZT6RY_SKoCPAkqZ3wmu4kdKWcoAz5VYqFBos9UjYd9AtKkow4TOxZCDT4FiAVfHa2DDowJCQ9FmX_CoEhI06_ud_AQbqMQ7eOdh3V9TRa64/s1600/a.png)
d. Opsi D benar, karena 1/x1 .1/x2=1/8 .1/(-2)=1/(-16)
Jawaban: -
17. Jika p dan q adalah akar-akar persamaan
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxgWbjyCYczcgSO1Q5f6Sgi_ZFEPpkPTRmGFBTbM7dvZjLf51jxLxwZ3lieKhHUE32XR0ARfQOrflSbtGEqS2qkBEZA7aVazOJqX2nOUXBF6zgf7yei2oAYI0VxiwxZNexk2XyezgJrnk/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjegwE3GNyZs8wK4oJV40kvTSF761lkFQoZmjH1xtM_fqdVibwTtXa5rUqLAKFmN-pCz6GNh2FtB1TFXAI35f4luKYtV6IX16ga2yTltQkr8YQUS4seUqH6vf0e7bBD0tMw-DiHTxJDHUQ/s1600/a.png)
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxgWbjyCYczcgSO1Q5f6Sgi_ZFEPpkPTRmGFBTbM7dvZjLf51jxLxwZ3lieKhHUE32XR0ARfQOrflSbtGEqS2qkBEZA7aVazOJqX2nOUXBF6zgf7yei2oAYI0VxiwxZNexk2XyezgJrnk/s1600/a.png)
p+q = -b/a = -(-5)/1 = 5
p.q = c/a = -1/1 = -1
PK dengan akar-akar 2p + 1 dan 2q + 1 adalah:
(2p + 1) + (2q + 1) = 2p + 2q + 2
= 2 (p + q) + 2
= 2 . 5 + 2
= 12
(2p + 1) (2q + 1) = 4pq + 2p + 2q + 1
= 4pq + 2 (p + q) + 1
= 4.(-1) + 2 (5) + 1
= -4 + 10 + 1
= 7
Jadi, PK yang baru adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgr_Vxb82at5124fKcSIvBwCS0o_sJxmOagLS2Hz_yfr1kU6iFQatekkJfh_0dL7m_jKdcBGiOEZPar9qPipMaaUhL8T9mFF2AHTRvgN9zWFwsAaftNd_D-XuaofPg7XYREeKMgobCXJ8g/s1600/a.png)
Jawaban: D
18. Akar-akar persamaan
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKPngQqm21qbG0rqVBnTXaNZX1jzmySigN3fAgslQfPZ9_n49lIhE599HFHEgo1HQP29BYxmPjSBRyRwI9U6Enx-l6CYTCyrysvEGH5QwXwHwIveNYIXeM3STxivGctigvP8QrxuR3Hbs/s1600/a.png)
a. 4
b. 2
c. -2
d. -6
e. -8
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKPngQqm21qbG0rqVBnTXaNZX1jzmySigN3fAgslQfPZ9_n49lIhE599HFHEgo1HQP29BYxmPjSBRyRwI9U6Enx-l6CYTCyrysvEGH5QwXwHwIveNYIXeM3STxivGctigvP8QrxuR3Hbs/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-AoSd-1ibOb2BuhJTpUbsIl8UWm-OBNLoMs2KtFInC6NV6Rj71lLnkDSLGv_dmquCU23SSq_eMnTXp2N7EKfWTsV09K4VS7VEl7NsAkj8EuE93BmFw6jZIuGM1RD3NoFKyKC8e3zc6Po/s1600/a.png)
p + q = -b/a = -p/1 = -p
p + 2q = 6
p + q + q = 6
(p + q) + q = 6
-p + q = 6
-(p – q) = 6
p – q = -6
Jawaban: D
19. Akar-akar persamaan kuadrat
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixR63XQ5J_EjsXg9N-Py-JL62qo1rLIeCpxMWrh-b1xojrOt_sX8b6FpUG9fpYQc7uMhnW1YOaqZgpEFGCw64P2k4-ctOqOREBuMWZuj-mtJppN9WI6rcfgV-IqvdnFg42SA3HMnoVMD0/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNsK9x-odiZsV4bGSjUoRGw5vOu44Qy5AOe3vX5ksaJVknXOcbDpxZFubiIscs_GrzLRw_pbivA8EFzSMQp_XooAx5oldXa_AoI5Ok64eHsMmMK2JZgT0KVnpu54Ex-O9kXEh1P_gITJw/s1600/a.png)
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixR63XQ5J_EjsXg9N-Py-JL62qo1rLIeCpxMWrh-b1xojrOt_sX8b6FpUG9fpYQc7uMhnW1YOaqZgpEFGCw64P2k4-ctOqOREBuMWZuj-mtJppN9WI6rcfgV-IqvdnFg42SA3HMnoVMD0/s1600/a.png)
Persamaan kuadrat di atas memiliki akar α dan β, maka:
α + β = -b/a = -(-12)/3 = 4
α . β = c/a = 2/3
akar-akar baru adalah (α + 2) dan (β + 2), maka:
(α + 2) + (β + 2) = α + β + 4
= 4 + 4
= 8
(α + 2) . (β + 2) = α . β + 2α + 2β + 4
= α . β + 2(α + β) + 4
= 2/3 + 2.4 + 4
= 2/3 + 8 + 4
= 2/3 + 12
= 2/3 + 36/3
= 38/3
Maka, persamaan kuadrat yang baru adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLzRPrNtNBDkeP_YpwWTxB-dYyjdoLB08VLp7XLr2sMH6BFcRvUS3w-miCz33RXJxdqvo9X7vmR7x1BhmMM_iuDvgO1sM6jjxY5WMGKpDIFE-zZ-Af-Z2qw0mtGZ4U3Ndp6yZuQYvFrik/s1600/a.png)
Jawaban: A
20. Akar-akar persamaan
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEOETlSIPs8X_oBLFYwmtWYIVu0qahDrOY3xVKyq6adQLMcT4lhYnjxk_V-a1HKE_CLKHWlHq3Pzb48xaHAWWHOBZfqzco8fi4tmwSkpJsfojUrh7NgMqrWXGiyJz90zkPiy3aopiaq2E/s1600/a.png)
a. -5
b. -4
c. 2
d. 3
e. 4
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEOETlSIPs8X_oBLFYwmtWYIVu0qahDrOY3xVKyq6adQLMcT4lhYnjxk_V-a1HKE_CLKHWlHq3Pzb48xaHAWWHOBZfqzco8fi4tmwSkpJsfojUrh7NgMqrWXGiyJz90zkPiy3aopiaq2E/s1600/a.png)
Persamaan kuadrat tersebut memiliki akar p dan q, dimana p > 0 dan q < 0, maka:
p + q = -b/a = -(2a - 3)/1 = -2a + 3
p . q = c/a = 18/1 = 18
karena p =2q maka:
p . q = 18
2q . q = 18
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja-c0alHLEfdJWU1v_lL8FFSsCecPoMq6S7yLNb6S1w6vo4IXxn9OlWB1Twaz237Jx8tipsg7llvcpZJ1z7g66RYy_zDi6Y-hn_PVjNDI_GSQYU0z77t9TF68nfYVCgM9i-rPiOoZv_Dw/s1600/a.png)
q = √9
q = 3
Karena p = 2q, maka p = 2 . 3 = 6
Nilai a adalah:
p + q = -2a + 3
6 + 3 = -2a + 3
9 = -2a + 3
2a = 3 – 9
2a = -6
a = -6/2
a = -3
nilai dari a – 1 = -3 – 1 = -4
jawaban: B
21. Akar-akar persamaan
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHvfA8wlVYcHunZ3vno3YLEaXwzNJCnQneIZGv62BxXQqkv_BaKfc5T8PVXvAjzEBTlLilvpcBuvWLy7zDfVXm14pTzfoWfuolBtxGEhE17SAEe3G2BSApFUlkY57EQC3f7L4zoo3oPjE/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTQNeZpBrNvOR5H3VlCoF8gpDXvSgiFaO8wgLLdAWC9pqcYyx7Q-tLpQ49GeQuUzl_t8oDBuLYv6Spq_ZxnlOKxXBfO-9JPemJ_NLEUyUMffmtd8efc3wVOmOIQCR615oD0tIpTgmsuTw/s1600/a.png)
a. -7
b. -2
c. 2
d. 3
e. 7
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHvfA8wlVYcHunZ3vno3YLEaXwzNJCnQneIZGv62BxXQqkv_BaKfc5T8PVXvAjzEBTlLilvpcBuvWLy7zDfVXm14pTzfoWfuolBtxGEhE17SAEe3G2BSApFUlkY57EQC3f7L4zoo3oPjE/s1600/a.png)
Persamaan kuadrat di atas memiliki faktor α dan β, maka:
α + β = -b/a = -(-a – 3)/1 = a + 3
α . β = c/a = 4a/1 = 4a
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiopO4a15P57u2YEjs-aEPi9iue2DX00ybD31iqtZ8NkJalTPzXEqFr8kNQhOrr5qwOxOnzjg4pUiggPYQtX-FNdVvdwW5Fj_4bI3868D-6vQHZg2O4o_Nrr5c4MYUKfNAHDgrgR3f1vAc/s1600/a.png)
Mencapai nilai minimum ketika a = -b/2a = -14/2.1 = -7
Jawaban: A
22. Garis y = 2x + k memotong parabola
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9Xb_BqPriBhe16wJ3Rsq-d1dPWu0wTVo3LlB0RphJNZcrPsOtrypB4yHr7lxHgT6eV9oLRZ843oPK5717gIQ5o72dGIWHxDoGZ6weWCCaPm9PcErvYqXIvGphPBdYK3mPLkN_48wXKek/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTrqP8NXeqsuBCIYdWnZIP0vnpiFePzpUaf4YUfZ4ujblrlZ0J0KxxjkoPi8Bc5_ZeNUIlo3L_Aq-u2e3Lv3dygxHlO-HJj9rLFf5GjvPYCzPkyJag9HZZi2ZHK_fP7egVK7b6uRNghDw/s1600/a.png)
a. -1
b. 0
c. 1
d. 2
e. 3
Pembahasan:
Karena Garis y = 2x + k memotong parabola
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9Xb_BqPriBhe16wJ3Rsq-d1dPWu0wTVo3LlB0RphJNZcrPsOtrypB4yHr7lxHgT6eV9oLRZ843oPK5717gIQ5o72dGIWHxDoGZ6weWCCaPm9PcErvYqXIvGphPBdYK3mPLkN_48wXKek/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRoJJbnziy_0u68HmBXoVXhGkjoUjpyAsgsDW7e7I3GWE0thuctocaUXdAJLpKsvnmcGdO9jq6h2exvNx8kRSaRVI0Zw_s0lYeUA_zaxXd_hdD115sx90_UMI_2TyL4T3UZ46tdOcncEc/s1600/a.png)
Karena berpotongan di (x1,y1) dan (x2,y2), maka akar-akar dari persamaan kuadrat tersebut adalah x1 dan x2, maka:
x1 + x2 = -b/a = -(-3)/1 = 3
x1 . x2 = c/a = 3 - k/1 = 3 – k
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhsXJ5QNWW5DcFYvNyn0PiQSorEZYmaMIbQtjqZQdpcYabsExkQKeJkrass_fbI8n_q5G0qtexGSFZWDkfkHizu2II1C7Pt1BD9kO5yu8U2UbIQlqm8jtu38hqOW27yCfe-WPxmNbPqf9k/s1600/a.png)
= 9 – 6 + 2k = 7
= 3 + 2k = 7
= 2k = 7 – 3
= 2k = 4
= k = 4/2
= k = 2
Jawaban: D
23. Kedua persamaan
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvMlVjxnikph_DbuHIbJUXzfmUT9E7TzZxK2pitPjuzQvCgvA7b8OlXR_aTvDt0iSQyQia9SwSLyTSIrIA_P6vJUz97-Cn8WzXetPqpKkdAJpCiDsX53bIseotqSLtCR9_EhsGKQlQ3yo/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1yLXhq0eEQF0YwcnhysP6f3RbRQ8W6LyXTHQV4R1KDJqSn_F4OaKNAkM99hX7RDtludQH7N91EbS00wCxo6Jax5p2Eb8cv8xd07ZYwqWAnuM67FbxW8OpHwsMLmQGAaPLBsY6u3h_q14/s1600/a.png)
a. -1/2 ≤ k ≤ 2
b. -1/4 ≤ k ≤ 1
c. -1/8 ≤ k ≤ 1
d. -1/8 ≤ k ≤ 2
e. -1/8 ≤ k ≤ 1
Pembahasan:
Persamaan kuadrat memiliki akar-akar real jika memenuhi D ≥ 0, maka:
Untuk persamaan
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvMlVjxnikph_DbuHIbJUXzfmUT9E7TzZxK2pitPjuzQvCgvA7b8OlXR_aTvDt0iSQyQia9SwSLyTSIrIA_P6vJUz97-Cn8WzXetPqpKkdAJpCiDsX53bIseotqSLtCR9_EhsGKQlQ3yo/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgC9oHML0tic6ioHoss8lF7hnA_LeuLAEteyDoY6lzALC9oTuxbNJqYsZB54UUX136Kf0Fx3NHnKJiWWRdemEQAlItM64K2Kt1Vam9PbwiroWRKxPnYAvfGEpAmKIauBh1bC2OKPCgNdDY/s1600/a.png)
4 – 4k ≥ 0
-4k ≥ -4
k ≤ -4/-4
k ≤ 1
untuk persamaan
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1yLXhq0eEQF0YwcnhysP6f3RbRQ8W6LyXTHQV4R1KDJqSn_F4OaKNAkM99hX7RDtludQH7N91EbS00wCxo6Jax5p2Eb8cv8xd07ZYwqWAnuM67FbxW8OpHwsMLmQGAaPLBsY6u3h_q14/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNMDpPixPBMy_4XUuonRYb0ExVIoRRT2psJcSK5Ohyphenhypheng8fg88pOuimGzw0JLD5FHwTDuzHsTsKkokhE1kZ4M3y6xouUmx2FTV6FY-UOxxA4IsOE819stRfjbb8EsNJv0a9501CITIPHczc/s1600/a.png)
1 + 8k ≥ 0
8k ≥ -1
k ≥ -1/8
jadi, nilai k yang memenuhi adalah -1/8 ≤ k ≤ 1
jawaban: C
24. Himpunan penyelesaian persamaan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSwjQ0v4OBE-8rkjdNszf-xvyACtW6j91c4LKoUfmF0NZFv3rvICS1rQZtWQJLT84Jl6BiQNO3KqkEi1rtD3W0sj3SNfGKA-t-91SVE3MHNDbjhlm2btjBuLjDWDEoeX3vmec24dMONVM/s1600/a.png)
a. Φ
b. {0}
c. {-2}
d. {0, -2}
e. {0, 2}
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtW4gweJXkAsZZjkpu_gcFKXUF26CT7Biv7R5LNv3suTMZEhV7de3n3ruja3_hOGVXV50KsoNdXzrjpjKuSRFsbbP3UhRgXe4bX96iTtd58_FFvyVe4F1Y4QsONygVMQUwmJSknr6Kkck/s1600/a.png)
x (x+2)=0
x = 0 atau x = -2
jawaban: D
25. Diberikan persamaan kuadrat
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_kZap3W9WwafskvMiNgNvQkdIUWvUrns7tKc8cI0h9BurzQLQM3X1MWpmM_3i7WOnENE7rHGnfjc8dY1ZwBGgkPoSj8-UfP1L4xXG060UjLBpNMWP4bOsnrMxlkP2Aoz8XkPvEh8lfdM/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEht4A2H0v3LSypXuF21Bdskts7j9H43Xv7Hsm7vC80SGV97H8hjyRjIxa0C2sRQt0pGmNkPI2YN8mOHM3agQd7SoRMMeuQdxi-Q3gYRXbe-z1qvskLOSVP7EMUyHHuOB2DwhGNXuphVUSk/s1600/a.png)
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_kZap3W9WwafskvMiNgNvQkdIUWvUrns7tKc8cI0h9BurzQLQM3X1MWpmM_3i7WOnENE7rHGnfjc8dY1ZwBGgkPoSj8-UfP1L4xXG060UjLBpNMWP4bOsnrMxlkP2Aoz8XkPvEh8lfdM/s1600/a.png)
Maka:
p + q = -b/a
4q + q = -b/a
5q = -b/a
q = -b/5a
p . q = c/a
4q . q = c/a
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5TpGo-FL9YQXjvxlA1r2d09OOJYg26HKaduWgGSvwAI8ITbMGEKLFBsLVQqkkbyO6Rjt3GOw5obV1BvQEXZXSKOQaTiJSIBdBmZqMkFWbg5OgVqvz3ENhEjP2aa_8sIx_GH0LBETenBM/s1600/a.png)
Jawaban: E
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