Question:
The sum of the zero and the product of zero of a quadratic polynomial are $\frac{-1}{2}$ and $-3$ respectively, write the polynomial.
Solution:
We can find the quadratic polynomial if we know the sum of the roots and product of the roots by using the formula
$x^{2}-$ (Sum of the zeros) $x+$ Product of zeros
$\Rightarrow x^{2}-\left(-\frac{1}{2}\right) x+(-3)$
$\Rightarrow x^{2}+\frac{1}{2} x-3$
Hence, the required polynomial is $x^{2}+\frac{1}{2} x-3$.
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