Question

Akar akar persamaan kuadrat 2x²+x-1=0 adalah alpha dan betha. persamaan kuadrat yang akar-akarnya (alpha+2) dan (Betha+2) adalah...

Answer 1

2x² + x - 1 = 0
( 2x - 1 ) ( x + 1 ) = 0

2x - 1 = 0
2x = 1
x = 1/2

x + 1 = 0
x = -1

alpha + 2 = 1/2 + 2 = 2 1/2 = 5/2
beta + 2 = -1 + 2 = 1

x = 5/2
2x = 5
2x - 5 = 0

x = 1
x - 1 = 0

persamaan kuadrat nya :
( 2x - 5 ) ( x - 1 ) = 0
2x² - 2x - 5x + 5 = 0
2x² - 7x + 5 = 0