Pertanyaan

Persamaan kuadrat 2 x 2 + ( 4 + a ) x + 2 a = 0 mempunyai akar-akar x 1 dan x 2 . Jika x 1 + x 2 = 8 maka nilai ∣ x 1 − x 2 ∣

Persamaan kuadrat $2 x^{2} + (4 + a) x + 2 a = 0$ mempunyai akar-akar $x_{1}$ dan $x_{2}$ . Jika $x_{1} + x_{2} = 8$ maka nilai $∣ x_{1} - x_{2} ∣$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Cari nilai Di dapatkan maka, 2 x 2 + ( 4 + a ) x + 2 a 2 x 2 + ( 4 − 20 ) x + 2 ( − 20 ) 2 x 2 + ( − 16 ) x − 40 2 x 2 − 16 x − 40 x 2 − 8 x − 20 ( x + 2 ) ( x − 10 ) x + 2 x x − 10 x = = = = = = = = = = 0 0 0 0 0 0 0 − 2 0 10 Di dapatkan x 1 = − 2 dan x 2 = 10 ∣ x 1 − x 2 ∣ = = = ∣ − 2 − 10 ∣ ∣ − 12 ∣ 12 Jadi, nilai adalah . Oleh karena itu, jawaban yang tepat adalah B.

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x squared plus open parentheses 4 plus a close parentheses x plus 2 a end cell equals 0 row cell a x squared plus b x plus c end cell equals 0 row a equals 2 row b equals cell 4 plus a end cell row c equals cell 2 a end cell end table

Cari nilai x subscript 1 plus x subscript 2 equals 8

$table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 plus x subscript 2 end cell equals cell fraction numerator negative b over denominator a end fraction end cell row 8 equals cell fraction numerator negative left parenthesis 4 plus a right parenthesis over denominator 2 end fraction end cell row cell 8 times 2 end cell equals cell negative 4 minus a end cell row 16 equals cell negative 4 minus a end cell row cell 16 plus 4 end cell equals cell negative a end cell row 20 equals cell negative a end cell row a equals cell negative 20 end cell end table$

Di dapatkan a equals negative 20 maka,

$2 x^{2} + (4 + a) x + 2 a 2 x^{2} + (4 - 20) x + 2 (- 20) 2 x^{2} + (- 16) x - 40 2 x^{2} - 16 x - 40 x^{2} - 8 x - 20 (x + 2) (x - 10) x + 2 x x - 10 x = = = = = = = = = = 0000000 - 2 010$