Question

If the roots of the equation $l{x}^2+nx+n$ = 0, l ¹ 0 are in the ratio p : q, then ${\left(p/q\right)}^{1/2}+{\left(q/p\right)}^{1/2}+{\left(n/l\right)}^{1/2}$

• A. $\frac{n}{l}$​
• B. 2${\left(\frac{n}{l}\right)}^{1/2}$
• C. 0
• D. None of these

Answer 1

The correct option is C

0

α+β = $\frac{-n}{l}$ , αβ=$\frac{n}{l}$ , $\frac{\alpha }{\beta }$= $\frac{p}{q}$

therefore ${\left(\frac{p}{q}\right)}^{1/2}$+${\left(\frac{q}{p}\right)}^{1/2}$ + ${\left(\frac{n}{l}\right)}^{1/2}$ = $\frac{\sqrt{\alpha }}{\sqrt{\beta }}$ + $\frac{\sqrt{\beta }}{\sqrt{\alpha }}$+$\sqrt{\alpha \beta }$

=$\frac{\alpha +\beta +\alpha \beta }{sqrt\alpha \beta }$ = $\frac{\frac{-n}{l}+\frac{n}{l}}{\sqrt{\alpha \beta }}$ = 0