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Question: If a,b are the roots of ax<sup>2</sup> + bx + b = 0, then \(\sqrt{\frac{\alpha}{\beta}} + \sqrt{\fra...

If a,b are the roots of ax2 + bx + b = 0, then αβ+βα+ba\sqrt{\frac{\alpha}{\beta}} + \sqrt{\frac{\beta}{\alpha}} + \sqrt{\frac{b}{a}}is equal to –

A

0

B

1

C

2

D

2ba2\sqrt{\frac{b}{a}}

Answer

0

Explanation

Solution

αβ\sqrt{\frac{\alpha}{\beta}}+ βα+ba\sqrt{\frac{\beta}{\alpha}} + \sqrt{\frac{b}{a}}

Ž α+βαβ\frac{\alpha + \beta}{\sqrt{\alpha\beta}}+ ba\sqrt{\frac{b}{a}}

Ž −b/ab/a+ba\frac{- b/a}{\sqrt{b/a}} + \sqrt{\frac{b}{a}} Ž −ba+ba- \sqrt{\frac{b}{a}} + \sqrt{\frac{b}{a}}= 0