Detection of positive roots of a polynomial with five parameters

摘要

We give a complete set of discriminatory criteria for a polynomial with five parameters to have a positive root. This polynomial arises from the characteristic equation of a difference equation Δ~n(x_k + px_(k-τ) + qx_(k-σ) = 0, which is used to model population dynamics. Our investigations are self-contained and based on the theory of envelopes.