A) \[\frac{2b}{ac}\]
B) \[\frac{2b}{\sqrt{ac}}\]
C) \[-\frac{2b}{\sqrt{ac}}\]
D) \[\frac{-b}{\sqrt{2}}\]
Correct Answer: C
Solution :
Given equation is\[a{{x}^{2}}+2bx+c=0\]. So \[\alpha +\beta =-\frac{2b}{a}\]and \[\alpha \beta =\frac{c}{a}\] Now\[\sqrt{\left( \frac{\alpha }{\beta } \right)}+\sqrt{\left( \frac{\beta }{\alpha } \right)}=\frac{\alpha +\beta }{\sqrt{\alpha \beta }}=\frac{-2b/a}{\sqrt{c/a}}=-\frac{2b}{\sqrt{ac}}\].
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