$1-$ Consider a negative unity$-$feedback control system as shown below.

a$)$ Construct the root$-$locus diagram. Determine all the important features like asymptotes, break$-$away and$/$or break$-$in points, imaginary$-$axis crossings, angle of arrivals and$/$or departures. $(25$pts$)$

b$)$ Determine all, the values of $K$ such that the closed$-$loop system is asymptotically stable. $(10$pts$)$