Question

If the ratio of the polynomial P (s) and its derivative gives a continued fraction expansion with ________ coefficients, then the polynomial P (s) is Hurwitz.

(a) all negative

(b) all positive

(c) positive or negative

(d) positive and negative

The question was asked in class test.

The doubt is from Hurwitz Polynomials in section Elements of Realizability and Synthesis of One-Port Networks of Network Theory

Answer 1

Right choice is (b) all positive

The best explanation: If the ratio of the polynomial P (s) and its derivative P^‘(s) gives a continued fraction expansion with all positive coefficients, then the polynomial P (s) is Hurwitz. If all the quotients in the continued fraction expansion are positive, the polynomial P(s) is positive.