Since \( \Large \alpha \) and \( \Large \beta \) are the roots by \( \Large ax^{2}+bx+c=0 \)

=> \( \Large \alpha + \beta \) = \( \Large -\frac{b}{c} \) and \( \Large \alpha \beta = \frac{c}{a} \)

Let the roots of \( \Large cx^{2}+bx+a=0 \) be \( \Large \alpha' \), \( \Large \beta' \) then

\( \Large \alpha' \) + \( \Large \beta' \) = \( \Large -\frac{b}{c} \) and \( \Large \alpha . \beta = \frac{a}{c} \)

Now, \( \Large \frac{ \alpha + \beta }{ \alpha \beta }=\frac{\frac{-b}{a}}{\frac{c}{a}}=\frac{-b}{c} \)

=> \( \Large \frac{1}{ \alpha }+\frac{1}{ \beta }= \alpha' + \beta' \)

Hence, \( \Large \alpha' \) = \( \Large \frac{1}{ \alpha } \) and \( \Large \beta' \) = \( \Large \frac{1}{ \beta } \)