Three coefficients of a polynomial can determine its instability (Q5955648)

The paper investigates relationships between the coefficients of a polynomial and the location of its roots, a problem of high relevance when studying stability of dynamical systems. In the case of Hurwitz stability (location of the roots in the left half-plane) it is shown that a sufficient condition for instability can be formulated as a very simple inequality satisfied by three coefficients only, independently of the degree of the polynomial. Is it also shown that if we know only two coefficients, it is not possible to conclude about instability. For more results along this direction, the reader is advised to consult the paper [\textit{A. V. Lipatov} and \textit{N. I. Sokolov}, Autom. Remote Control 39, 1285-1291 (1978; Zbl 0427.93040)], unfortunately missing from the list of references.