Find a quadratic polynomial, the sum and product of whose zeroes are -8 and 12 respectively. Hence find the zeroes.

Solution

Let Sum of zeroes (α + β) = S = -8 …[Given]
Product of zeroes (αβ) = P = 12 …[Given]
Quadratic polynomial is x² – Sx + P
= x² – (-8)x + 12
= x²+ 8x + 12
= x² + 6x + 2x + 12
= x(x + 6) + 2(x + 6)
= (x + 2)(x + 6)
Zeroes are:
x + 2 = 0 or x + 6 = 0
x = -2 or x = -6