Consider the unity feedback negative system with an open-loopfunction G(s)= K (s^2+10s+24)/(s^2+3s+2).
a. Plot the locations of open-loop poles with X and zeros with Oon an s-plane.
b. Find the number of segments in the root locus diagram basedon the number of poles and zeros.
c. The breakaway point (the point at which the two real polesmeet and diverge to become complex conjugates) occurs when K =0.02276. Show that the closed-loop system has repeated poles forthis K.
d. The break-in point (the point at which the complex conjugatepoles meet and diverge to become real) occurs when K = 10.97. Showthat the closed-loop system has repeated poles for this K.
e. Find the poles of the closed-loop system when K = 6.
f. Sketch the two segments of the root locus.
g. Check your work using MATLAB. It is not necessary to submitthe output.
