Question

Agar persamaan kuadrat (x-2a)²+x+a-4=0 mempunyai akar kembar, maka nilai a adalah…
A. -17/12
B. -15/12
C. -13/12
D. 15/12
E. 17/12

Answer 1

D = 0
b² - 4ac = 0
(-4m√2)² - 4 (4) (-3m +2) = 0
32 m² +48 m -32 = 0
2m² + 3m - 2 = 0
(2m -1)(m + 2) = 0
m = 1/2 atau m = -2

Answer 2

Syarat akar kembar, D = 0

(x - 2a)² + x + a - 4 = 0
x² - 4ax + 4a² + x + a - 4 = 0
x² - 4ax + x + 4a² + a - 4 = 0
x² + (1 - 4a)x + 4a² + a - 4 = 0

a = 1
b = 1 - 4a
c = 4a² + a - 4

b² - 4ac = 0
(1 - 4a)² - 4(1)(4a² + a - 4) = 0
1 - 8a + 16a² - 16a² - 4a + 16 = 0
-12a + 17 = 0
-12a = -17
12a = 17
a = 17/12
→ E.