This paper is a study of some properties of the zero distributions of Hurwitz polynomials and also of polynomials $H_r (x)$ of the form $H_r (x) = x^r F(x) + G(x)$, where $F(x)$, $G(x)$ are independent of r particular, it is proved that if a sequence of strict Hurwitz polynomials $Q_r (z)$ satisfies $Q_r (z)Q_r ( - z) = H_r (x)$, $x = - z^2 $, then an increasing number of the zeros of both the odd part and even part of $Q_r (z)$ become arbitrarily small and arbitrarily great as $r \to \infty $. This theorem has application in network theory as the guarantor of the validity of a new synthesis method for realizing quite general filters by means of a transformerless, inductance, capacitance ladder network terminated in resistance (LC-R ladders). A special case of the theorem has been used to validate a method of even part synthesis of an arbitrary impedance by means of at most four LC-R ladder networks.