Question

If $\alpha =-5$ and $\beta =9$ then form the quadratic equation.

Answer 1

$\Rightarrow$ let $\alpha$ and $\beta$ are roots.

$\Rightarrow$ $\alpha =-5,\beta =9$

$\Rightarrow$ Sum of the roots $=\alpha +\beta =-5+9=4$

$\Rightarrow$ Product of the roots $=\alpha .\beta =-5\times 9=-45$

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

$\Rightarrow$ $x^2-\left(4\right)x+(-45)=0$

$\therefore$ $x^2-4x-45=0$

$\therefore$ Required quadratic equation is $x^2-4x-45=0$