Question

Write a quadratic polynomial, the sum and product of whose zeroes are $3$ and$-2$ respectively.

Answer 1

Finding the required polynomial:

Sum of zeroes, $\alpha +\beta =3$

Product of zeroes, $\alpha \beta =-2$

The formula to form a quadratic polynomial is,

$\begin{array}{rcl}& & \begin{array}{c}{x}^2-(\alpha +\beta )x+\left(\alpha \beta \right)\\ =x^2-3x-2\end{array}\begin{array}{}\\ \end{array}\end{array}$

Hence, the required quadratic polynomial is $x^2-3x-2$.