Assume that you have a system with two poles at s = -1, s = -3, 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.
• Plot the root locus (i.e. location of poles for all positive gains) on the plot below.