Question

If alpha and beta are zeroes of the polynomial ax^2 + bx+c then value of root over of alpha / beta +root over of beta /alpha

Answer 1

α and β are the roots of $ax^2 + bx + c = 0$

Then $\alpha + \beta = \frac{-b}{a}$ and $\alpha\beta = \frac{c}{a}$

$\sqrt{ \frac{\alpha}{\beta} } + \sqrt{\frac{\beta}{\alpha}}$

$\frac{ \sqrt{\alpha} }{ \sqrt{\beta} } + \frac{ \sqrt{\beta} }{ \sqrt{\alpha} }$

$\frac{\alpha + \beta }{ \sqrt{\alpha\beta} }$

$\frac{ \frac{-b}{a} }{ \sqrt{ \frac{c}{a} } }$