Question

If $\alpha ,\beta$ are the roots of $a{x}^2+bx+c=0$ then find the values of
$\frac{1}{\alpha }+\frac{1}{\beta }$

Answer 1

Equation $a{x}^2+bx+c=0$

If $\alpha$ and $\beta$ are the roots of given equation

then sum of roots $\alpha +\beta =\frac{-b}{a}$

Product of roots $\alpha \beta =\frac{c}{a}$

Hence $\frac{1}{\alpha }+\frac{1}{\beta }=\frac{\alpha +\beta }{\alpha \beta }=\frac{-b}{a}\times \frac{a}{c}=\frac{-b}{c}$