Example $5\mathrm{.}1$: Control System Stability

Consider the feedback control system with the following transfer functions:

$G_p=G_d=\frac{1}{5s+1},G_m=\frac{1}{s+1},G_v=\frac{1}{2s+1}$ and $G_c=k_c$

The transfer function for set$-$point

Substitute $(5\mathrm{.}1)$ into $(5\mathrm{.}2)$ and rearrange:

$Y(s)=\frac{K_c((s)+1)}{10s^3+17s^2+8(s)+1+K_c}$

Find analyzing the roots of the cubic polynomial?