Question

Persamaan kuadrat yang akar akarnya 5 kurangnya dari dua kali persamaan x^2 - 5x + 6 = 0 adalah ...

Answer 1

(x-2))(x-3)
itu persamaan kuadratnya

Answer 2

X^2 - 5x + 6 = 0
misal akarnya p dan q, maka
p+q = -b/a = 5
p.q = c/a = 6

Persamaan kuadrat yg akar2nya 5 kurang dr akar pers kuadrat diatas
p' = 2p - 5
p = ( p' + 5)/2

q' = 2q - 5
q = (q' + 5)/2

p + q = 5
(p' + 5)/2 +(q' + 5)/2 = 5
(p' + q' + 10)/2 = 5
p' + q' + 10 = 10
p' + q' = 0

p . q = 6
(p' + 5)/2 . (q' + 5)/2 = 6
(p'.q' + 5(p' + q') + 25)/4 = 6
(p' . q' + 5(0) + 25) = 24
p' . q' = -1

Pers kuadrat baru =
x^2 - (p' + q')x + p'q'
= x^2 + 0x + (-1)
= x^2 - 1

Semoga membantu :)