Question

The quadratic polynomial having product of zeroes $-1$ and sum of zeroes $\frac{1}{2}$ is ____

• A. $2x^2-x-2$
• B. $2x^2+x-2$
• C. $2x^2-x+2$
• D. $x^2-x-2$

Answer 1

The correct option is A $2x^2-x-2$

Given, Sum of zeroes, $\alpha +\beta =\frac{1}{2}$
Product of zeroes, $\alpha \beta =-1$

We know,
Quadratic equation given its zeroes is,
$k[x^2-(\alpha +\beta )x+(\alpha \beta \left)\right]\Rightarrow x^2-(\alpha +\beta )x+\left(\alpha \beta \right)$

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

$\therefore$ Polynomial is $2x^2-x-2$