Question

If the ratio of the roots of $l{x}^2+nx+n=0$ is p:q, then

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Let the roots be $\alpha and\beta$ $Then,\alpha +\beta =\frac{-n}{1};\alpha \beta =\frac{n}{1}and\frac{\alpha }{\beta }=\frac{p}{q}$ $Now,\sqrt{\frac{p}{q}}+\sqrt{\frac{q}{p}}+\sqrt{\frac{n}{1}};and\sqrt{\frac{\alpha }{\beta }}+\sqrt{\frac{\beta }{\alpha }}+\sqrt{\alpha \beta }=\frac{\alpha +\beta +\alpha \beta }{\sqrt{\alpha \beta }}=\frac{-\frac{n}{1}+\frac{n}{1}}{\sqrt{\frac{n}{1}}}=0$