Question

If the zeros of the polynomial $f\left(x\right)=k^2{x}^2-17x+k+2,(k>0)$ are reciprocal of each other, then the value of $k$ is

• A. $2$
• B. $-1$
• C. $-2$
• D. $1$

Answer 1

The correct option is A $2$

Let $\alpha$ and $\frac{1}{\alpha }$ be the roots of $k^2{x}^2-17x+(k+2)$
So, product of roots $=\alpha \times \frac{1}{\alpha }$
$\Rightarrow \alpha \times \frac{1}{\alpha }=\frac{k+2}{k^2}$
$\Rightarrow k^2=k+2$
$\Rightarrow k^2-k-2=0$
$\Rightarrow k=2$ and $k=-1$
But $k>0,\therefore k=2$
Hence, option $A$ is the correct answer.