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Polynomials with multiple zeros

Published online by Cambridge University Press:  26 February 2010

R. Güting
R. Güting
Affiliation:
Department of Mathematics, Makerere University College, Kampala, Uganda.
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Extract

Estimates involving polynomials can often naturally be given in terms of the discriminants of these polynomials or of the resultants of pairs of polynomials. Since the discriminant of a polynomial with multiple zeros vanishes as does the resultant of two polynomials with common zeros these results become trivial when applied to such polynomials or pairs of polynomials. Therefore it is often necessary to exclude polynomials with multiple zeros from a given investigation. In theoretical studies of a measure-theoretical nature this often does not affect the results; however for the purpose of constructing polynomials with specified properties it can be an advantage if it is not necessary to restrict the attention to polynomials without multiple zeros.

Type
Research Article
Information
Mathematika , Volume 14 , Issue 2 , December 1967 , pp. 181 - 196
Copyright
Copyright © University College London 1967

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References

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