Question

Let $p,q\ne 0$ and let the roots of the equation $x^2+px+q=0$ be $\alpha ,\beta$ then find the equation whose roots are $\frac{1}{\alpha },\frac{1}{\beta }$.

Answer 1

Given the roots of the equation $x^2+px+q=0$ be $\alpha ,\beta$.......(1).

To find the equation whose roots are $\frac{1}{\alpha },\frac{1}{\beta }$ let us put $\frac{1}{x}$ in stead of $x$ in (1).

Then we get,

$\frac{1}{x^2}+p\frac{1}{x}+q=0$

or, $q{x}^2+px+1=0$

This is the required equation.