jika x1 dan x2 adalah akar persamaan kuadrat x2-5x+10=0,maka 1 per x1+2 dan 1 per x2+2

Persamaan Kuadrat

x² - 5x + 10 = 0
x1 + x2 = -b/a = -(-5)/1 = 5
x1.x2 = c/a = 10

Akar2 PK baru :
1/(x1 + 2) dan 1/(x2 + 2)

p = 1/(x1 + 2) + 1/(x2 + 2)
p = (x2 + 2 + x1 + 2)/(x1 + 2)(x2 + 2)
p = (x1 + x2 + 4) / (x1x2 + 2(x1 + x2) + 4)
p = 9/24 = 3/8

q = 1/(x1 + 2) × 1/(x2 + 2)
q = 1/(x1x2 + 2(x1 + x2) + 4)
q = 1/24

PK baru :
x² - px + q = 0
x² - 3/8 x + 1/24 = 0
24x² - 9x + 1 = 0 ✔

cara cepat
Akar PK : x1 + 2 dan x2 + 2
PK :
(x - 2)² - 5(x - 2) + 10 = 0
x² - 9x + 24 = 0

Akar PK : 1/(x1 + 2) dan 1/(x2 + 2)
Posisi a dan c, dibalik
x² - 9x + 24 = 0
24x² - 9x + 1 = 0 ✔