Question

If one root of the equation $4x^2-2x+(\beta -4)=0$ be the reciprocal of the other, then find $\beta$

Answer 1

Let roots be $\alpha$ and $\frac{1}{\alpha }$

$4x^2-2x+\beta -4=0$

Product of Roots$=\alpha .\frac{1}{\alpha }=\frac{\beta -4}{4}$

$1=\frac{\beta -4}{4}$

$\therefore \beta =8$