jika p dan q akar akar persamaan kuadrat 3x^2+6x+4=0, maka persamaan kuadrat yang mempunyai akar akar 2p+q+1 dan p+2q+1 adalah

3x^2 + 6x + 4 = 0
p + q = -b/a = -6/3 = -2
pq = c/a = 4/3
p^2 + q^2 = (p + q)^2 - 2pq = (-2)^2 - 2(4/3) = 4 - 8/3 = 4/3

Misal : m = (2p + q + 1) dan n = (p + 2q + 1)

m + n = (2p + q + 1) + (p + 2q + 1)
= 3p + 3q + 2
= 3(p + q) + 2
= 3(-2) + 2
= -6 + 2
= -4

mn = (2p + q + 1)(p + 2q + 1)
= 2p^2 + 4pq + 2p + pq + 2q^2 + q + p + 2q + 1
= 2p^2 + 2q^2 + 5pq + 3p + 3q + 1
= 2(p^2 + q^2) + 5pq + 3(p + q) + 1
= 2(4/3) + 5(4/3) + 3(-2) + 1
= 8/3 + 20/3 - 6 + 1
= 28/3 - 5
= 13/3

Persamaan kuadrat baru
x^2 - (m + n)x + mn = 0
x^2 - (-4)x + 13/3 = 0
3x^2 + 12x + 13 = 0