$($a$)$ Find the breakaway points on the root locus and the value of gain at those points.

$($b$)$ In the design of ventilators, it is very important to have negligible overshoot with

the fastest possible settling time. It has been suggested that a value of K $=5\mathrm{.}35$

will achieve these specifications. Mark the position of the closed$-$loop poles for this

value of K and explain why this is a reasonable gain choice.