If the roots of $x^3-14x^2+56x-64=0$ are in G.P then the middle root is

The given equation is $x^3-14x^2+56x-64=0$

Given that the roots are in G.P.,

So, let  the roots are $\frac{\alpha }{\beta },\alpha ,\alpha \beta$

$\therefore$  product of the roots $\frac{\alpha }{\beta }.\alpha .\alpha \beta =64$

$\Rightarrow {\alpha }^{\text{3}}=64$

$\Rightarrow \alpha =4$

the middle root is $\left(\alpha \right)=4$