Question

A quadratic polynomial, whose zeroes are $-3$ and $4$ is

• A. $x^2-x+12$
• B. $x^2+x+12$
• C. $\frac{x^2}{2}-\frac{x}{2}-6$
• D. $2x^2+2x-24$

Answer 1

The correct option is C

$\frac{x^2}{2}-\frac{x}{2}-6$

Explanation for Correct option:

Let $\alpha ,\beta$ be the zeroes of quadratic polynomial such that $\alpha =-3,\beta =4$

Sum of zeroes,

$\alpha +\beta =-3+4=1$

Product of Zeroes,

$\alpha \beta =-3\times 4=-12$

Therefore, the quadratic polynomial can be expressed as,

$x²-(sumofzeroes)x+(productofzeroes)$

$\begin{array}{rcl}& =& x²-(\alpha +\beta )x+\left(\alpha \beta \right)\\ & =& x²–\left(1\right)x+(-12)\\ & =& x²–x-12\end{array}$

On dividing by $2$ we get,

$\begin{array}{rcl}& =& \frac{x²}{2}–\frac{x}{2}-\frac{12}{2}\\ & =& \frac{x^2}{2}-\frac{x}{2}-6\end{array}$

Thus, the required polynomial is$\frac{x^2}{2}-\frac{x}{2}-6$

Hence the correct option is (C)