Question

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

Answer 1

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

Let $a,b$ be roots

$b=\frac{1}{a}$

$\therefore a\cdot \frac{1}{a}=\frac{\beta -4}{4}$

$\therefore \beta =8$