Question

The sum of the zeros and the product of zeros of a quadratic polynomial are $\frac{-1}{2}and-3$ respectively. Write the polynomial.

Answer 1

Given the sum of zeroes: $(\alpha +\beta )=\frac{-1}{2}$

Product of zeroes: $\left(\alpha \beta \right)=-3$

Recall that the quadratic polynomial with zeroes $\alpha ,\beta$ is given by $x^2-(\alpha +\beta )x+\left(\alpha \beta \right)$

$\Rightarrow x^2-\left[\frac{-1}{2}\right]x+(-3)$

$\Rightarrow x^2+\left(\frac{1}{2}\right)x-3$