On the zeros of polynomials: An extension of the Eneström–Kakeya theorem

This paper presents an extension of the Eneström–Kakeya theorem concerning the roots of a polynomial that arises from the analysis of the stability of Brown ( K , L ) methods. The generalization relates to relaxing one of the inequalities on the coefficients of the polynomial. Two results concerning the zeros of polynomials will be proved, one of them providing a partial answer to a conjecture by Meneguette (1994) [6].