Question

If one zero of $p\left(x\right)=(a^2+a)x^2+45x+6a$ is resiprocal of other ,find a.

Answer 1

Let one solution =t

then other solution will be, 1/t

In quadratic equation $a{x}^2+bx+c$ product of roots is given by$\frac{c}{a}$

So,

$\begin{array}{c}t\times \frac{1}{t}=\frac{6a}{a^2+a}\\ 1=\frac{6}{a+1}\\ a+1=6\\ a=5\end{array}$

Thus value of a=5