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 `α + β = (-1)/2`

Product of the quadratic polynomial is `αβ = -3`

Let S and P denote the sum and product of the zeros of a polynomial as `(-1)/2 `and –3.

Then

The required polynomial `g(x)` is given by

`g(x)=k (x^2-Sx +p)`

`=k[x^2-((-1)/2)x+(-3)]`

`= k [x^2+1/2x-3]`

Hence, the quadratic polynomial is `g(x)=k (x^2+x/2-3)`, where k is any non-zero real number.