Question

Akar-akar persamaan 2x²-5x-6=0 adalah α dan β. persamaan kuadrat baru yang akar-akarnya (α-3) dan (β-3) adalah...
a. 2x² - 7x + 3 = 0
b. 2x² + 7x + 3 = 0
c. 2x² + 7x - 3 = 0
d. 2x² - 7x + 9 = 0
e. 2x² - 7x - 9 = 0

Answer 1

2x^2-5x-6 = 0
a = 2
b = -5
c = -6
*mempermudah pembacaan...
x1 = p
x2 = q
------
p+q = -b/a = 5/2
p.q = c/a = -6/2 = -3

akar baru :
(p-3) = m
(q-3) = n

m+n = p+q-3 = (5/2)-6 = -7/2
m.n = (p-3)(q-3) = pq-3(p+q)+9
•••••••••••••••••••••• = (-3)-3(5/2)+9
•••••••••••••••••••••• = (-3)-(15/2)+9
•••••••••••••••••••••• = (-6-15+18)/2
•••••••••••••••••••••• = -3/2

persamaan =

x^2 -(m+n)x + (m.n) = 0
x^2 -(-7/2)x + (-3/2) = 0
x^2 +7/2x -3/2 = 0
----------------------------- x 2
2x^2 +7x -3 = 0