An Asymptotic Property of the Roots of Polynomials

Hermann Flaschka
1971 Proceedings of the American Mathematical Society  
It is shown that if the imaginary parts of the roots \j(s) of a polynomial P(A, s), s(£R", are unbounded for large |i|, then they are in fact unbounded along a one-parameter algebraic curve 5 =s(R). The result may be used to reduce certain questions about polynomials in several variables to an essentially one-dimensional form; this is illustrated by an application to hyperbolic polynomials.
doi:10.2307/2036474 fatcat:3pfd75hjnnfrtot33xjbmn3vw4