For each of the following loop transfer function f(s), find the portion of the root locus on the real axis, asymptotes, the arrival and departure angles at any complex zero or pole, and the frequency of any imaginary-axis crossing. plot the sketch of the root locus based on above findings. verify your results using matlab. submit plots of your hand sketches and the matlab results.
a. f(s)=- s(s+1)(s +5)(8 +10)
b. f(s)=; s +2 s(s+1)(3+5)(8+10) (s+2)(s+6)
c. f(s)= (+1)(3+5)(s+10)