Question

If $\alpha$ and $\beta$ are the zeroes of ${5x}^2-7x+1=0$. Find the value of $\frac{1}{\alpha }+\frac{1}{\beta }$.

Answer 1

Sum of the roots$=\alpha +\beta =\frac{7}{5}$

Product of the roots$=\alpha \beta =\frac{1}{5}$

$\frac{1}{\alpha }+\frac{1}{\beta }=\frac{\alpha +\beta }{\alpha \beta }$

$=\frac{\frac{7}{5}}{\frac{1}{5}}$

$=\frac{7}{5}\times 5=7$

$\therefore \frac{1}{\alpha }+\frac{1}{\beta }=7$