Question

# If a and $$\beta$$ are the roots of the equation $$ax^2+2bx+c=0$$, then $$\sqrt {a/\beta}+\sqrt {\beta /a}$$ is equal to

A
2bc
B
2bac
C
2bac
D
bac

Solution

## The correct option is D $$\dfrac {-2b}{\sqrt {ac}}$$$$\alpha ,\beta$$ are roots of $$a{ x }^{ 2 }+2bx+c=0$$$$\alpha +\beta =\cfrac { -2b }{ a } ,\alpha \beta =\cfrac { c }{ a }$$$$\sqrt { \cfrac { \alpha }{ \beta } } +\sqrt { \cfrac { \beta }{ \alpha } } =\cfrac { \alpha +\beta }{ \sqrt { \alpha \beta } }$$$$=\cfrac { \cfrac { -2b }{ a } }{ \sqrt { \cfrac { c }{ a } } }$$$$\therefore \sqrt { \cfrac { \alpha }{ \beta } } +\sqrt { \cfrac { \beta }{ \alpha } } =\cfrac { -2b }{ \sqrt { ac } }$$Mathematics

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