Question

Zeroes of quadratic polynomials are given on the left. Match them with the respective quadratic polynomials.

• A. $x^2-2x-24$
• B. $x^2-10x+25$
• C. $64x^2-1$
• D. $x^2+x-30$

Answer 1

We know,
$f\left(x\right)=\left[\right(x^2-(\alpha +\beta )x+(\alpha \times \beta )]$

$\text{I}.\alpha =6\&\beta =-4:$
Sum of zeroes, $\alpha +\beta =2$
Product of zeroes, $\alpha \times \beta =-24$
$\therefore f\left(x\right)=x^2-2x-24$

$\text{II}.\alpha =5\&\beta =5:$
Sum of zeros, $\alpha +\beta =10$
Product of zeros, $\alpha \times \beta =25$
$\therefore f\left(x\right)=x^2-10x+25$

$\text{III}.\alpha =\frac{-1}{8}\&\beta =\frac{1}{8}$
Sum of zeros, $\alpha +\beta =0$
Product of zeros, $\alpha \times \beta =-\frac{1}{64}$
$\therefore f\left(x\right)=64x^2-1$

$\text{IV.}\alpha =5\&\beta =-6$
Sum of zeros, $\alpha +\beta =-1$
Product of zeros, $\alpha \times \beta =-30$
$\therefore f\left(x\right)=x^2+x-30$