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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
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B
2bac
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C
2bac
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D
bac
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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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