Question

Find the value of $m$ for which the roots of the quadratic equation $x^2-2(5+2m)x+3(7+10m)=0$ will be reciprocal to each other.

Answer 1

Let $\alpha ,\frac{1}{\alpha }$ be the roots of the equation $x^2-2(5+2m)x+3(7+10m)=0$.

Then from the relation between the roots and co-efficient we get,

$\alpha .\frac{1}{\alpha }=3(7+10m)$

or, $30m=-20$

or, $m=-\frac{2}{3}$.