Consider the points (s_{1}=-3+j 4) and (s_{2}=-3-j 2) in the (s)-plane. Then, for a system with the

Question:

Consider the points $s_{1}=-3+j 4$ and $s_{2}=-3-j 2$ in the $s$-plane. Then, for a system with the open-loop transfer function:

\[
\mathrm{G}(s) \mathrm{H}(s)=\frac{\mathrm{K}}{(s+1)^{4}}
\]

(a) $s_{1}$ is on the root locus, but not $s_{2}$

(b) $s_{2}$ is on the root locus, but not $s_{1}$

(c) both $s_{1}$ and $s_{2}$ are on the root locus

(d) neither $s_{1}$ nor $s_{2}$ is on the root locus.