For the sixth-order polynomials a(s) and b(s), the Hurwitz stability of their convex combination is necessary and sufficient for the existence of a polynomial c(s) such that c(s)/a(s) and c(s)/b(s) are both strictly positive real. Then, this result is generalized to polynomial segments of arbitrary order. The provided method is constructive, and is insightful and helpful in solving the general robust strictly positive real synthesis problem.