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
B
1α,1β
C
1α,1β
D
1α,1β

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 $$\displaystyle \dfrac { 1 }{ \alpha } ,\dfrac { 1 }{ \beta }$$.Maths

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