Question

Akar akar persamaan 2 - 5x - 6 = 0 adalah α dan β. Persamaan kuadrat baru yang akar akarnya ( α - 3 ) dan ( β - 3 ) adalah...
A. 2 - 7x + 3 = 0
B. 2 + 7x + 3 = 0
C. 2 + 7x - 3 = 0
D. 2 - 7x + 9 = 0
E. 2 - 7x - 9 = 0

Answer 1

cara 1
x²-5x-6 = 0
a = 1, b = -5, c = -6

α+β = -b/a = -(-5)/1 = 5
αβ = c/a = -6/1 = -6

persamaan kuadrat baru akar-akarnya adalah (α-3) dan (β-3)
misal akar-akarnya
x1 = (α-3)
x2 = (β-3)

x1+x2 = (α-3)+(β-3) = α+β-6 = 5-6 = -1
x1 . x2 = (α-3)(β-3) = αβ-3α-3β+9 = αβ-3(αβ)+9 = -6-3(5)+9 =-12

pers. kuadrat baru tsb dapat kita tulis
x²-(x1+x2)x+x1.x2 = 0
x²-(-1)x -12 = 0
x²+x-12 = 0

cara 2
kita cari nilai α dan β
x²-5x-6 = 0
(x-6)(x+1) = 0
x-6 = 0 -----------> x = α = 6
x+1 = 0 ----------> x = β = -1

α-3 = 6-3 = 3
β-3 = -1-3 = -4

pers kuadrat baru :
x²-(3+(-4))x+(3)(-4) = 0
x²+x-12 = 0

(jawaban tidak ada pada opsi)