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Question

If $$\alpha$$ and $$\beta$$ are the roots of equation $$ax^2 + bx + c = 0$$, then the roots of equation $$cx^2 + bx + a = 0$$ are 


A
1α,1β
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B
1α,1β
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C
1α,1β
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D
1α,1β
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Solution

The correct option is A $$\displaystyle{\frac{1}{\alpha}, \frac{1}{\beta}}$$
As $$\alpha ,\beta $$ are roots of $${ ax }^{ 2 }+bx+c=0$$

Replacing $$\displaystyle x\rightarrow \dfrac { 1 }{ x } $$, we get

$$\displaystyle a{ \left( \dfrac { 1 }{ x }  \right)  }^{ 2 }+b\left( \dfrac { 1 }{ x }  \right) +c=0$$

$$\Rightarrow { cx }^{ 2 }+bx+c=0$$
Hence, roots are $$\displaystyle \dfrac { 1 }{ \alpha  } ,\dfrac { 1 }{ \beta  } $$.

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