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

Quadratic equation with $\alpha$ and $\beta$ as roots can be written as

$x^2-(\alpha +\beta )+\alpha \beta =0$

Here, $\alpha =-3$ and $\beta =4$

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

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

$\therefore$ The quadratic equation is

$x^2-(\alpha +\beta )x+\alpha \beta =0$

$\Rightarrow x^2-1x-12=0$

$\Rightarrow \frac{x^2}{2}-\frac{x}{2}-\frac{12}{2}=0$

$\Rightarrow \frac{x^2}{2}-\frac{x}{2}-6=0$

Hence the quadratic polynomial is $\frac{x^2}{2}-\frac{x}{2}-6$