Question

If $x^3+2x^2-4x+5=-$ has roots $\alpha ,\beta$ and $\gamma$, then value of $\frac{({\alpha }^3+5)({\beta }^3+5)({\gamma }^3+5)}{13\alpha \beta \gamma }$ is equal to

Answer 1

Cubic equation: For cubic equation

of the form $a{x}^3+b{x}^2+cx+d=0,$ if $\alpha ,\beta$

$\gamma$ are roots.

$\alpha +\beta +\gamma =\frac{b}{a};\alpha \beta +\beta \gamma +\gamma \alpha =\frac{c}{a};$

$\alpha \beta \gamma =-\frac{d}{a}$