The sum and product of the zeros of a quadratic polynomial are -1/2 and -3 respectively. What is the quadratic polynomial?

Question

The sum and product of the zeros of a quadratic polynomial are - \(\frac{1}{2}\) and - 3 respectively. What is the quadratic polynomial?

Answer 1

Given,

Sum of zeroes (α + β) = − (1/2)

Product of zeroes (αβ) = −3

As we know that the quadratic polynomial with zeroes α, β is given by;

x ² − (α + β)x + (αβ)

= x² − [−(1/2)]x + (−3)

= x² + (1/2)x – 3