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General Solution of Cos theta = Cos alpha

If α, β a...

Question

If $α$ , $β$ are the roots of the equation $a x^{2} + b x + b = 0$ , then what is the value of $\sqrt{\frac{α}{β}} + \sqrt{\frac{β}{α}} + \sqrt{\frac{b}{a}}$ ?

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Solution

The correct option is B $0$
Here,
$α + β = - \frac{b}{a} α β = \frac{b}{a}$

So,

$\sqrt{\frac{α}{β}} + \sqrt{\frac{β}{α}} + \sqrt{\frac{b}{a}}$

$= \frac{α + β}{\sqrt{α β}} + \sqrt{α β}$

$= \frac{α + β + α β}{\sqrt{α β}}$

$= \frac{\frac{- b}{a} + \frac{b}{a}}{\frac{b}{a}} = 0$

Hence, option B is correct.

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