Let $a, \beta$be roots of $a{x}^2+bx+c=0,$ where 

$ac\ne 0.$ Roots of $a{x}^2+bx+c=0$ are

$\alpha +\beta =-b/a,\alpha \beta =c/a$

$\begin{array}{l}\text{Now, }\frac{b}{c}=-\frac{b/a}{c/a}=-\frac{\alpha +\beta }{\alpha \beta }\\ =\left(-\frac{1}{\alpha }\right)+\left(-\frac{1}{\beta }\right)\\ \text{And }\frac{a}{c}=\frac{1}{\alpha \beta }=\left(-\frac{1}{\alpha }\right)\left(-\frac{1}{\beta }\right)\end{array}$

$\text{ Thus, roots of }c{x}^2-bx+a=0\text{ are }-1/\alpha ,-1/\beta$