Question

The loop transfer function of an LTI system is G(s)H(s) =K(s+1)(s+5)/s(s+2)(s+3). For K>0, the point on the real axis that does not belong to the root locus of the system is

(a) -0.5

(b) -2.5

(c) -3.5

(d) -5.5

I got this question by my school principal while I was bunking the class.

The origin of the question is Construction of Root Loci in chapter The Root Locus Technique of Control Systems

Answer 1

Correct choice is (c) -3.5

Easiest explanation: The points present on the root locus are right to the odd number of poles and zeroes.