Question

Jika p dan q adalah akar-akar persamaan 2x²-3x-5=0, maka persamaan kuadrat yang akar-akarnya (2+1/p) dan (2+1/q) adalah.......
bantu jawab pliiiss

Answer 1

Persamaan kuadrat
x² - (x1+x2)x + x1×x2 = 0
x1 = 2+1/p
x2 = 2+1/q
p+q = -b/a = -(-3)/2 = 3/2
p.q = c/a = -5/2
x1 + x2 = 2+1/p + 2+1/p
4 + 1/p+1/q
= 4 + (p+q / p.q)
= 4 + (3/2 / -5/2)
= 4 + (3/2 × 2/-5)
= 4 + (-3/5)
= 20/5 - 3/5 = 17/5
x1 × x2 = (2+1/p)(2+1/q)
= 4 + 2/p + 2/q + 1/p.q
= 4 + 2(1/p+1/q) + 1/(-5/2)
= 4 + 2(17/5) - 2/5
= 20/5 + 34/5 - 2/5 = 52/5
x² - 17/5x + 52/5 = 0
------------------------------ × 5
5x² - 17x + 52 = 0