Question

If the ratio of the roots of the equation ${lx}^2+nx+n=0$ be $p:q$, then $\sqrt{\frac{p}{q}}+\sqrt{\frac{q}{p}}+\sqrt{\frac{n}{l}}=$

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (A)

$0$

Given equation,
$l{x}^2+nx+n=0$
Let $\alpha ,\beta$ be the roots of the equation,
$\alpha +\beta =-\frac{n}{l},\alpha \beta =\frac{n}{l}$
Also, given $\frac{\alpha }{\beta }=\frac{p}{q}$
Consider, $\sqrt{\frac{p}{q}}+\sqrt{\frac{q}{p}}+\sqrt{\frac{n}{l}}$
$=\sqrt{\frac{\alpha }{\beta }}+\sqrt{\frac{\beta }{\alpha }}+\sqrt{\alpha \beta }$
$=\frac{\alpha +\beta +\alpha \beta }{\sqrt{\alpha \beta }}$
$=\frac{-\frac{n}{l}+\frac{n}{l}}{\sqrt{\alpha \beta }}$
$=0$