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.

Answer 1

We can find the quadratic polynomial if we know the sum of the roots and product of the roots by using the formula
x² − (Sum of the zeros)x + Product of zeros
$$\begin{gathered} \Rightarrow x^2-\left(-\frac{1}{2}\right)x+\left(-3\right) \\ \Rightarrow x^2+\frac{1}{2}x-3 \end{gathered}$$
Hence, the required polynomial is $x^2+\frac{1}{2}x-3$.

⇒x2−2√x+13=0⇒3x2−32√x+1=0