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

We can find the quadratic polynomial if we know the sum of the roots and product of the roots by using the formula

$\mathrm{x}^{2}-($ sum of the zeroes $) \mathrm{x}+$ product of zeroes

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

$\Rightarrow x^{2}+\frac{1}{2} x-3$

Hence, the required polynomial is $x^{2}+\frac{1}{2} x-3$.