Question

Find a quadratic polynomial whose zeroes are $-4$ and $-5$.

Answer 1

Find the sum and product of the roots of the quadratic equation.

Let $\alpha$and $\beta$ be the roots of the quadratic equation.

Sum of the zeroes

$$\begin{gathered} \Rightarrow \alpha +\beta =-4-5 \\ \Rightarrow \alpha +\beta =-9 \end{gathered}$$

Product of the zeroes

$\Rightarrow \alpha \beta =20$

Substitute these values in the standard quadratic equation $x^2-\left(\alpha +\beta \right)x+\alpha \beta =0$.

$\Rightarrow x^2+9x+20=0$

Hence, the quadratic equation is $x^2+9x+20=0$.