Question

For real roots of sk, all the quotients of s in s^2+ωk^2 of the polynomial P (s) are __________

(a) negative

(b) non-negative

(c) positive

(d) non-positive

This question was addressed to me by my school teacher while I was bunking the class.

This intriguing question comes from Hurwitz Polynomials in portion Elements of Realizability and Synthesis of One-Port Networks of Network Theory

Answer 1

Correct choice is (b) non-negative

To elaborate: For real roots of sk, all the quotients of s in s^2+ωk^2 of the polynomial P (s) are non-negative. So by multiplying all factors in P(s) we find that all quotients are positive.