Roughly sketch the root locus with respect to \(K\) for the equation of \(1+K L(s)=0\) and the following choices for \(L(s)\). Make sure to give the asymptotes, arrival or departure angles, and points crossing the imaginary axis. Verify your results using MATLAB.

a. \(L(s)=\frac{1}{(s+1)(s+3)}\)

b. \(L(s)=\frac{1}{(s+1)(s+3)(s+7)}\)

c. \(L(s)=\frac{s+5}{(s+1)(s+3)(s+7)}\)

d. \(L(s)=\frac{s(s+5)}{(s+1)(s+3)(s+7)}\)