QUESTION $4$

A system has a transfer function: $T(s)=\frac{1}{s^3+5s^2+20s+6}$

$($a$)$ Determine whether the system is stable,

$[7$ marks$]$

$($b$)$ Determine the roots of the characteristic equation,

$[7$ marks$]$

$($c$)$ Plot the response of the system to a unit step input.

$[6$ marks$]$