Question

If the zeros of polynomial $k^2{x}^2-16(k+x)+k+2,(k<0)$ are reciprocal of each other, then the value of $k$ is:

[1 mark]

• A. -1
• B. 1
• C. 0
• D. 2

Answer 1

The correct option is A -1

We know that,
Product of roots = 1 ($\because$ Roots are reciprocal of each other.)
$\text{Product of the roots}=\frac{\text{Constant term}}{\text{Coefficeint of}{x}^2}$
$\frac{(k+2)}{k^2}=1k+2=k^2$
$\Rightarrow k^2-k-2=0\Rightarrow k^2+k-2k-2=0\Rightarrow k(k+1)-2(k+1)=0\Rightarrow (k+1)(k-2)=0\Rightarrow k=-1,2\therefore k=-1(\because k<0)$