Given a unity$-$feedback system with the following $G(s)$ :

$G(s)=\frac{K}{(s+3)(s+5)}$

a$.$ Please sketch the root locus of the system. Compute manually where the root locus will be on the real axis, and also the asymptotes $($if there are any$).$

b$.$ Can this system be unstable? Please explain your answer!

c$.$ Explain why the system cannot operate with a settling time of $\frac{2}{3}$ second and a percent overshoot of $1\mathrm{.}5\%$ with a simple gain K adjustment

d$.$ Please design a controller so that the system can achieve the performance parameters as described in point $($b$).$ What kind of controller is needed? Please explain the way.