Question

Find the quadratic polynomial, the sum of whose zeros is 0 and their product is –1. Hence, find the zeros of the polynomial.

Answer 1

Given: Sum of zeros = 0, Product of zeros = –1.

For a monic quadratic with zeros α and β we have f(x) = x² – (α + β)x + αβ. 

Substitute α + β = 0 and αβ = –1: 

f(x) = x² – 0 × x + (–1) 

= x² – 1 

Solve f(x) = 0:

x² – 1 = 0 

⇒ (x – 1)(x + 1) = 0

⇒ x = 1 or x = –1

The required quadratic polynomial is x² – 1 and its zeros are 1 and –1.