Complex Numbers And Quadratic Equations question 541
Question: If $ \alpha $ and $ \beta $ are roots of $ ax^{2}+2bx+c=0 $ , then $ \sqrt{\frac{\alpha }{\beta }}+\sqrt{\frac{\beta }{\alpha }} $ is equal to [BIT Ranchi 1990]
Options:
A) $ \frac{2b}{ac} $
B) $ \frac{2b}{\sqrt{ac}} $
C) $ -\frac{2b}{\sqrt{ac}} $
D) $ \frac{-b}{\sqrt{2}} $
Show Answer
Answer:
Correct Answer: C
Solution:
Given equation is $ ax^{2}+2bx+c=0 $ . So $ \alpha +\beta =-\frac{2b}{a} $ and $ \alpha \beta =\frac{c}{a} $ Now $ \sqrt{( \frac{\alpha }{\beta } )}+\sqrt{( \frac{\beta }{\alpha } )}=\frac{\alpha +\beta }{\sqrt{\alpha \beta }}=\frac{-2b/a}{\sqrt{c/a}}=-\frac{2b}{\sqrt{ac}} $ .
BETA
