Question

Find a quadratic polynomial whose zeroes are $-3$ and $4$.

Answer 1

Solve for 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

$$\begin{gathered} \Rightarrow \alpha +\beta =-3+4 \\ \Rightarrow \alpha +\beta =1 \end{gathered}$$

Product of the zeroes

$\Rightarrow \alpha \beta =-12$

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

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

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