Question

Find a quadratic polynomial whose zeroes are $2$ and$-6$.

Answer 1

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

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

Sum of the zeroes

$$\begin{gathered} \alpha +\beta =2+(-6) \\ \alpha +\beta =-4 \end{gathered}$$

Product of the zeroes

$\alpha \beta =2\times \left(-6\right)=-12$

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

$\Rightarrow x^2+4x-12=0$

Hence, the quadratic equation is $x^2+4x-12=0$.