Question

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

• A. $\alpha ,\beta$
• B. $\frac{1}{\alpha },\frac{1}{\beta }$
• C. ${\alpha }^2,{\beta }^2$
• D. none of these

Answer 1

The correct option is B $\frac{1}{\alpha },\frac{1}{\beta }$

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

Now we are to find the roots of the equation $q{x}^2+px+1=0$.......(2)

Now replacing $x$ by $\frac{1}{x}$ in equation (1) we get,

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

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

So equation (2) is obtained by putting $\frac{1}{x}$ in (1).

So the roots of the equation (2) will be $\frac{1}{\alpha },\frac{1}{\beta }$.