Question

Find the quadratic polynomial, the sum and product of whose zeroes are –3 and 2 respectively. Hence find the zeroes.

Answer 1

Given, sum of zeroes = –3 and product of zeroes = 2

The quadratic polynomial will be x² – (sum of zeroes)x + product of zeroes = 0

⇒ x² – (–3)x + 2 = 0

⇒ x² + 3x + 2 = 0

⇒ x² + 2x + x + 2 = 0

⇒ x(x + 2) + 1(x + 2) = 0

⇒ (x + 2)(x + 1) = 0

∴ x + 2 = 0 and x + 1 = 0

⇒ x = –2 and x = –1

Hence, zeroes are –2 and –1.