Question

If one zero of the polynomial $f\left(x\right)=(k^2+4)x^2+13x+4k$ is reciprocal of the other, then k is equal to __________.

• A. $2$
• B. $-2$
• C. $1$
• D. $-1$

Answer 1

The correct option is A $2$

Let's assume the roots of the polynomial be $\alpha ,\frac{1}{\alpha }$

Product of the roots of the polynomial $=\frac{4k}{k^2+4}$

$\Rightarrow \alpha \times \frac{1}{\alpha }=\frac{4k}{k^2+4}$

$\Rightarrow \frac{4k}{k^2+4}=1$

$\Rightarrow 4k=k^2+4$

$\Rightarrow k^2-4k+4=0$

$\Rightarrow (k-2{)}^2=0$

$\Rightarrow k=2$