Question

If one zero of the polynomial $\left(a^2-9\right)x^2+13x+60$ is reciprocal of other the value of $a.$

Answer 1

$(a^2-9)x^2+13x+60$

Let the root be $\alpha$, other reciprocal root will be $\frac{1}{\alpha }$

Product of roots in quadratic polynomial $=\frac{60}{a^2-9}$

$\frac{60}{a^2-9}=\alpha \times \frac{1}{\alpha }=1$

$⟹60=a^2-9$

$⟹a^2=69$

$⟹a=\pm \sqrt{69}$