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

Answer: (A)

2

$f\left(x\right)=k^2{x}^2-17x+k+2.(k>0)\left(given\right)$
Let $\alpha and\frac{1}{\alpha }$ are the roots
So, $\alpha \times \frac{1}{\alpha }=\frac{k+2}{k^2}$
$\Rightarrow k^2=k+2\Rightarrow k^2-k-2=0$
$\Rightarrow k=2and-1$
$\therefore k=2$