Question

Akar-akar persamaan x² + (a-2)x + a² -2a = 0 adalah p dan q. Jika p : q = 2 : 1 maka nilai p + q = ...

Answer 1

Verified answer

Jawab

x² + (a -2)x + (a²-2a)= 0

(i) p + q = - (a-2) = 2 -a
(ii) p q = a²- 2a
(iii) p : q = 2 :1

p = 2q sub ke 1
p+ q= 2- a
2q + q = 2 - a
2q = 2- a 
q= 1 - 1/2 a
 
p= 2q sub ke ii
p. q =  a² - 2a
2 q²= a²- 2a

2 (1- 1/2 a)² = a²  - 2a
2(1 - a + 1/4 a²) = a² - 2a
2 - 2a + 1/4a² = a² - 2a
8 - 8a + 2a² = 4a² -8a
2a² = 8
a²= 4
a= 2 atau a = -2

p+ q = 2- a
a= 2 -> p + q = 0
a= -2 --> p + q = - 4