Question

Jika x1 dan x2 adalah akar-akar persamaan kuadrat x^2 - 4x +3 = 0, maka persamaan kuadrat yang akar-akarnya x1^2 dan x1^2 adalah
A) x2 + 10x +9 = 0
B) x2 -10x +9 = 0
C) x2 + 4x +3 = 0
D) x2 - 4x +3 = 0
E) x2 - 4x - 9 = 0

Answer 1

X² - 4x + 3 = 0
(x - 3)(x - 1)

x - 3 = 0
x = 3

x - 1 = 0
x = 1

akar-akar yang baru :
x = 3²
x = 9
x - 9 = 0

x = 1²
x = 1
x - 1 = 0

(x - 9)(x - 1)
(=) x² - x - 9x + 9 = 0
(=) x² -10x + 9 = 0
---> B.

Answer 2

x1 + x2 = 4
x1 . x2 = 3

maka :
x1 = 1 ===> (x1)² = 1
x2 = 3 ===> (x2)² = 9


x² - ((x1)²+ (x2)²)x + ((x1)² . (x2)²) = 0
x² - (1 + 9)x + (1 x 9) = 0
x² - 10x + 9 = 0

===> B.