A Gauss-Lucas type theorem on the location of the roots of a polynomial

M.D Buhmann; T.J Rivlin

doi:10.1016/0021-9045(91)90020-B

Journal of Approximation Theory

Paper

01 Jan 1991

A Gauss-Lucas type theorem on the location of the roots of a polynomial

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Abstract

In this note, we prove a geometrical relationship between the zeros of a polynomial p of order m, say, and the zeros of another polynomial which is derived from p by multiplying each of p's coefficients, call them {αk}k = 0m, by a power of k or by k2 + 2kλ for λ > 0. © 1991.

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