Diketahui x1​ dan x2​ akar-akar persamaan ax2+bx+c=0. Jika x1​+2 dan x2​+2 akar-akar persamaan kuadrat ax2+px+q=0, maka q+p=...

Pertanyaan

Diketahui x subscript 1 space text dan end text space x subscript 2 akar-akar persamaan straight a x squared plus straight b x plus straight c equals 0. Jika x subscript 1 plus 2 space text dan end text space x subscript 2 plus 2 akar-akar persamaan kuadrat straight a x squared plus straight p x plus straight q equals 0, maka q plus p equals...

  1. straight c plus 3 straight b

  2. straight c minus straight b plus 4 straight a

  3. straight c minus straight b

  4. straight c minus straight b plus 8 straight a

  5. straight c plus 3 straight b plus 8 straight a

D. Enty

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Pertama, kita lihat persamaan kuadrat pertama, yaitu a x squared plus b x plus c equals 0 yang mempunyai akar-akar x subscript 1 dan x subscript 2. Sifat-sifat akar-akar persamaan tersebut:


x subscript 1 plus x subscript 2 equals negative straight b over straight a dan x subscript 1 times x subscript 2 equals straight c over straight a


Dimisalkan akar-akar dari persamaan kuadrat yang baru adalah alpha equals x subscript 1 plus 2 dan beta equals x subscript 2 plus 2. Untuk menyusun persamaan kuadrat yant baru, kita cari alpha plus beta dan alpha times beta.


table attributes columnalign right center left columnspacing 0px end attributes row cell alpha plus beta end cell equals cell open parentheses x subscript 1 plus 2 close parentheses plus open parentheses x subscript 2 plus 2 close parentheses end cell row blank equals cell x subscript 1 plus x subscript 2 plus 4 end cell row cell alpha plus beta end cell equals cell negative straight b over straight a plus 4 end cell row blank equals cell fraction numerator negative b plus 4 a over denominator a end fraction end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell alpha times beta end cell equals cell open parentheses x subscript 1 plus 2 close parentheses times open parentheses x subscript 2 plus 2 close parentheses end cell row blank equals cell x subscript 1 times x subscript 2 plus 2 x subscript 1 plus 2 x subscript 2 plus 4 end cell row blank equals cell x subscript 1 times x subscript 2 plus 2 open parentheses x subscript 1 plus x subscript 2 close parentheses plus 4 end cell row blank equals cell straight c over straight a plus 2 times open parentheses negative straight b over straight a close parentheses plus 4 end cell row cell alpha times beta end cell equals cell fraction numerator straight c minus 2 straight b plus 4 straight a over denominator straight a end fraction end cell end table


Persamaan kuadrat yang baru:


table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus open parentheses alpha plus beta close parentheses x plus open parentheses alpha times beta close parentheses end cell equals 0 row cell x squared minus open parentheses fraction numerator negative straight b plus 4 straight a over denominator straight a end fraction close parentheses x plus open parentheses fraction numerator straight c minus 2 straight b plus 4 over denominator straight a end fraction close parentheses end cell equals 0 row cell straight a x squared minus left parenthesis negative straight b minus 4 straight a right parenthesis x plus left parenthesis straight c minus 2 straight b plus 4 straight a right parenthesis end cell equals 0 row cell straight a x squared plus left parenthesis straight b minus 4 straight a right parenthesis x plus left parenthesis straight c minus 2 straight b plus 4 straight a right parenthesis end cell equals 0 row blank blank blank end table

Diperoleh

straight a x squared plus straight p x plus straight q equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight a x squared plus left parenthesis straight b minus 4 straight a right parenthesis x plus left parenthesis straight c minus 2 straight b plus 4 straight a right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table


Maka straight p equals straight b minus 4 straight a dan straight q equals straight c minus 2 straight b plus 4 straight a.


table attributes columnalign right center left columnspacing 0px end attributes row cell straight q plus straight p end cell equals cell open parentheses straight b minus 4 straight a close parentheses plus open parentheses straight c minus 2 straight b plus 4 straight a close parentheses end cell row blank equals cell open parentheses straight c minus straight b close parentheses end cell end table


Oleh karena itu, jawaban yang benar adalah C.

38

5.0 (2 rating)

Pertanyaan serupa

Akar-akar persamaan kuadrat x2 +2x+5=0 adalah α dan β. Persamaan kuadrat baru  yang akar-akarnya (α−1) dan (β−1) adalah...

164

5.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia