Question

If the polynomial P (s) is either even or odd, then the roots of P (s) lie on __________

(a) on σ axis

(b) on jω axis

(c) left half of s-plane

(d) right half of s plane

The question was asked during a job interview.

Question is taken from Hurwitz Polynomials in division Elements of Realizability and Synthesis of One-Port Networks of Network Theory

Answer 1

The correct option is (b) on jω axis

To elaborate: If the polynomial P (s) is either even or odd, then the roots of P (s) lie on jω axis not on right half of s plane or on left half of s-plane.