$14\mathrm{.}11$ for the control shown, the characteristics equation is

$s^4+4s^3+6s^2+4s+(1+k)=0$

$($a$)$ determine value of $k$ above which the system is unstable.

$($b$)$ Determine the value of $k$ for which the two of the roots are on the imaginary axis, and determine the values of these imaginary roots and remaining roots are real.

$s^4+4s^3+6s^2+4s+(1+k)=0$