Question

The roots of the quadratic equation $3x^2-2(7+9p)+(8-5p)=0$ are reciprocal to each other, then find the value fo $p$.

Answer 1

Let the roots of the given quadratic equation

$3x^2-2(7+9p)+(8-5p)=0$ be $\alpha ,\frac{1}{\alpha }$.

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

$\alpha .\frac{1}{\alpha }=\frac{(8-5p)}{3}$

or, $8-5p=3$

or, $5=5p$

or, $p=1$.