Find the polynomial, if the sum and the product of whose zeros are $-3$ and $2$ respectively.

Given :

The sum and the product of zeros of the polynomial are $-3$ and $2$.

To do :

We have to find the polynomial.

Solution :

Let $\alpha$ and $\beta$ are the roots of the required polynomial.

So, $\alpha + \beta = -3$

 $\alpha \times \beta = 2$

If $\alpha$ and $\beta$ are the roots of the polynomial, then the polynomial is,

$x^2 -(\alpha + \beta)x + ( \alpha \times \beta) = 0$

$x^2 - (-3)x +  2= 0$

$x^2 +3x + 2 = 0$

Therefore, the required polynomial is $x^2 +3x +2=0$.

Tutorialspoint

Updated on: 10-Oct-2022

143 Views

Kickstart Your Career

Get certified by completing the course

Get Started