Assume that you have a system with three poles at s = -1, -3, and -5, and a single zero at s = -2.  The G(s) for the system is:

The system is being controlled in a feedback system as shown below.

        You need to determine how the poles move in the s-plane as the gain, K, is varied.  (i.e. plot the root locus)

• Using analysis techniques, obtain an expression for the closed loop poles.
• Sketch the root locus on the plot below