Question

Form a quadratic polynomial sum of whose zeroes is 8 and their product is 12 find the zeroes of the polynomial

Answer 1

Let α and β be the roots of the quadratic equation.

α+β = 8

αβ = 12

Let p(x) be the quadratic equation

P(x) = {x^2 + (sum of roots)x + product of roots}

={x^2 + (α+β)x + αβ}

=(x^2+8x+12)

α+β = 8.............................(1)

αβ = 12

(α-β)^2 =( α+β)^2- 4αβ

=64-48

=16

(α-β) =4................................(2)

On adding (1) and (2)

α = 6

β = 2