Question

Find a quadratic polynomial, the sum and product of whose zeroes are -1/2 and -1/2 respectively.

Answer 1

Given: Sum of zeroes = α + β = -1/2

Product of zeroes = αβ = -1/2

Then, the quadratic polynomial

= x² – (sum of zeroes)x + product of zeroes

We can consider 2x² + x – 1 as required quadratic polynomial because it will also satisfy the given conditions.