Consider the following statements regarding root loci.
(1) All root loci start from the respective poles of G (s) H (s)
(2) All root loci end at the respective zeros of G(s) H(s) or go to infinity.
(3) The root loci are symmetrical about the imaginary axis of the S-plane.
Of these statements :
MH SET - 2018, SET Exam - 2018,
Answer: B
The keyed answer is 1 and 2 are correct.
Statement 1 is true: at K = 0 the closed loop poles coincide with the open loop poles, so each branch starts at a pole of G(s)H(s). Statement 2 is true: as K grows without bound, the branches approach the open loop zeros, and the excess branches go to infinity along asymptotes.
Statement 3 is false. The root locus is symmetrical about the real axis, because complex roots of a polynomial with real coefficients occur in conjugate pairs; there is no symmetry about the imaginary axis. So the options including 3 are wrong (the option printed '2 and B' is a misprint pairing).
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