Question

If one of the zeroes of the polynomial $f\left(z\right)=p^2{z}^2+8z+16$ is reciprocal of the other, then the value of $p$ is:

• A. $\pm 4$
• B. $-5$
• C. $6$
• D. $-1$

Answer 1

The correct option is A $\pm 4$

$\Rightarrow$ Let one root is $\alpha$ be the one zero then other zero will be $\frac{1}{\alpha }$

$\Rightarrow$ The given quadratic equation is $p^2{z}^2+8z+16$

$\Rightarrow$ Here, $a=p^2,b=8,c=16$

$\Rightarrow$ $\alpha \times \frac{1}{\alpha }=\frac{c}{a}$

$\Rightarrow$ $1=\frac{16}{p^2}$

$\Rightarrow$ $p^2=16$

$\therefore$ $p=\pm \sqrt{4}$