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

Let sum of quadratic polynomial is

Product of the quadratic polynomial is

Let S and P denote the sum and product of the zeros of a polynomial asand.

Then

The required polynomial is given by

Hence, the quadratic polynomial is, where k is any non-zero real number