Question

If the roots of the quadratic equation $l{x}^2+nx+n=0$ are $p$ and $q$, then the value of $\sqrt{\frac{p}{q}}+\sqrt{\frac{q}{p}}+\sqrt{\frac{n}{l}}$ is

• A. $1$
• B. $3$
• C. $0$
• D. $-1$

Answer 1

The correct option is C $0$

We have,

$l{x}^2+nx+n=0$

Since, $p$ and $q$ are the roots of this equation, then

$p+q=\frac{-n}{l}$

$pq=\frac{n}{l}$

Therefore,

$p+q=-pq$

$p+q+pq=0$

On dividing $\sqrt{pq}$, we get

$\sqrt{\frac{p}{q}}+\sqrt{\frac{q}{p}}+\sqrt{pq}=0$

$\sqrt{\frac{p}{q}}+\sqrt{\frac{q}{p}}+\sqrt{\frac{n}{l}}=0$

Hence, the value of $\sqrt{\frac{p}{q}}+\sqrt{\frac{q}{p}}+\sqrt{\frac{n}{l}}$ is $0$.