Question

Tentukan nilai K agar setiap persamaan berikut mempunyai akar kembar
1) x² + 3x + K = 0
2) Kx²+ (3K – 1 ) + K - 3 = 0

Answer 1

1. x^2 + 3x + k = 0
a = 1
b = 3
c = k

Syarat akar kembar:
D = 0
b^2 - 4ac = 0
3^2 - 4 . 1 . k = 0
9 - 4k = 0
9 = 4k
k = 9/4 = 2 1/4

2. kx^2 + (3k - 1)x + k - 3 = 0
a = k
b = 3k - 1
c = k - 3

Syarat akar kembar:
D = 0
b^2 - 4ac = 0
(3k - 1)^2 - 4 . k . (k - 3) = 0
9k^2 - 6k + 1 - 4k^2 + 12k = 0
5k^2 + 6k + 1 = 0
5k^2 + 5k + k + 1 = 0
5k(k + 1) + 1(k + 1) = 0
(k + 1)(5k + 1) = 0
k = -1 atau k = -1/5