Question

Akar-akar persamaan kuadrat x^2+4x+k=0 adalah x1 dan x2. Jika x1^2 - x2^2 = -32 maka k = ...
A. -12
B. -6
C. 6
D. 12
E. 24

Answer 1

Verified answer

X1^2 - x2^2 = (x1 + x2)(x1 - x2)

(x1 - x2)^2 = x1^2 + x2^2 - 2x1x2
(x1 - x2) = √(x1^2 + x2^2 - 2x1x2)

(x1 + x2)^2 = x1^2 + x2^2 + 2x1x2
x1^2 + x2^2 = (x1 + x2)^2 - 2x1x2


(x1 - x2) = √(x1^2 + x2^2 - 2x1x2) = √((x1 + x2)^2 - 2x1x2 - 2x1x2)
= √((x1 + x2)^2 - 4x1x2)

x1^2 - x2^2 = (x1 + x2)√((x1 + x2)^2 - 4x1x2)

x1 + x2 = -b/a = -4/1 = -4
x1.x2 = c/a = k/1 = k

(x1 + x2)√((x1 + x2)^2 - 4x1x2) = (-4)√((-4)^2 - 4.k) = -32
-4√(16 - 4k) = -32
√(16 - 4k) = 8
16 - 4k = 64
4k = 16 - 64
4k = -48
k = -12