${\alpha }_1,{\beta }_1\text{ are the roots of }a{x}^2+bx+c=0\text{ and }{\alpha }_2,{\beta }_2\text{ are the roots of }p{x}^2+qx+r=0.\text{ If }{\alpha }_1{\alpha }_2={\beta }_1{\beta }_2=1\text{ , then }$

${\alpha }_2=\frac{1}{{\alpha }_1}\text{ and }{\beta }_2=\frac{1}{{\beta }_1}$

$\text{ In other words the roots of }{2}^{\mathrm{nd}}\text{ equation are reciprocal of the roots of }{1}^{\text{st }}\text{ equation. So equations }c{x}^2+bx+a=0\text{ has roots }{\alpha }_2,{\beta }_2$

$\begin{array}{l}\text{ Hence it is same as }p{x}^2+qx+r=0\\ \text{ Comparing, }\frac{c}{p}=\frac{b}{q}=\frac{a}{r}\end{array}$