Question

Find a quadratic polynomial, whose zeroes are $-3\mathrm{and}4$.

Answer 1

Finding the quadratic equation:

If $\alpha \mathrm{and}\beta$ are the roots of a quadratic equation, then that equation can be written as:

$x^2-\left(\alpha +\beta \right)x+\alpha \beta =0$ …(1)

Here, $x$ is a variable.

It is given that $\alpha =-3\mathrm{and}\beta =4$, then the quadratic equation can be found by substituting the values of $\alpha \mathrm{and}\beta$ in equation (1):

$$\begin{gathered} x^2-\left(-3+4\right)x+4\left(-3\right)=0 \\ \Rightarrow x^2-x-12=0 \end{gathered}$$

Final Answer:

Hence, the quadratic equation, whose roots are $-3\mathrm{and}4$ is ${\mathit{x}}^{\mathbf{2}}\mathbf{-}\mathit{x}\mathbf{-}\mathbf{12}\mathbf{=}\mathbf{0}$.