Question

soove this question​

Answer 1

Answer:

Hello.

Hope this helps you.

Since the roots are in the ratio p : q, they are pa and qa, for some a.

The sum of the roots is

$pa + qa = -\frac{n}{\ell}$

and the product of the roots is

$pqa^2 = \frac{n}{\ell}$

So

$\displaystyle pa + qa + \frac{n}{\ell} = 0 \\ \\\Rightarrow p + q + \frac{n}{\ell a} = 0 \\ \\\Rightarrow p + q + \frac{n}{\ell \sqrt{\frac{n}{\ell pq}}} = 0 \\ \\\Rightarrow p + q + \frac{n\sqrt{\ell pq}}{\ell\sqrt{n}} = 0 \\ \\\Rightarrow p + q + \sqrt{\frac{n}{\ell}}\sqrt{pq} = 0 \\ \\\Rightarrow \frac{p}{\sqrt{pq}} + \frac{q}{\sqrt{pq}} + \sqrt{\frac{n}{\ell}} = 0 \\ \\\Rightarrow \sqrt{\frac{p}{q}}+\sqrt{\frac{q}{p}}+\sqrt{\frac{n}{\ell}} = 0$