Question

Find a quadratic polynomial,the sum and product of whose zeros are $-3$ &$2$

Answer 1

Let the zeroes be α and β

According to the question:

$\alpha +\beta =-3$and $\alpha \beta =2$

The quadratic polynomial whose sum and product of the zeroes are given is given by :

$x²-(\alpha +\beta )x+\alpha \beta$

⇒ Then the quadratic polynomial will be :

⇒ $x²-(-3)x+2$

⇒$x²+3x+2$

Hence, the quadratic polynomial is $x^2+3x+2$