Question

A quadratic equation whose roots are $\frac{a}{\sqrt{\left(a\right)}\pm \sqrt{(a-b)}}$, is

• A. $b{x}^2-2a\sqrt{a}x+a^2=0.$
• B. $b{x}^2+2a\sqrt{a}x+a^2=0.$
• C. $b{x}^2+2a\sqrt{a}x-a^2=0.$
• D. $b{x}^2-2a\sqrt{a}x-a^2=0.$

Answer 1

The correct option is A $b{x}^2-2a\sqrt{a}x+a^2=0.$

Given, a quadratic equation whose roots are $\frac{a}{\sqrt{\left(a\right)\pm (a-b)}}$

On rationalizing, the roots are $\frac{a}{b}[\sqrt{a}\pm \sqrt{a-b}]$

$\therefore$Sum of roots $=S=\frac{2a\sqrt{a}}{b},$ and Product of roots $=P=\frac{a^2}{b}$

Equation becomes,

$x^2-Sx+p=0$

$\Rightarrow x^2-\frac{2a\sqrt{a}}{b}x+\frac{a^2}{b}=0$

$\Rightarrow b{x}^2-2a\sqrt{a}x+a^2=0.$