The transfer function of a dynamic system is given by

\[G(s)=\frac{20 s+50}{s^{3}+10 s^{2}-5 s-30}\]

a. Using Routh's stability criterion, determine the stability of the open-loop system.

b. Suppose that a negative unity feedback is applied to this open-loop system. Using Routh's stability criterion, determine the stability of the resulting closed-loop system.

c. Using MATLAB, solve for the poles of the open and closed-loop systems and verify the results obtained in Parts (a) and (b).