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 $x_1\;\text{dan}\;x_2$ akar-akar persamaan $\mathrm ax^2+\mathrm bx+\mathrm c=0$ . Jika $x_1+2\;\text{dan}\;x_2+2$ akar-akar persamaan kuadrat $\mathrm ax^2+\mathrm px+\mathrm q=0$ , maka $q+p=...$

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

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

Oleh karena itu, jawaban yang benar adalah C.