Comments on ‘ On the number of roots of an algebraic equation contained between given limits, by C. Hermite ’

B. D.O. Anderson

doi:10.1080/00207177808922427

Comments on ‘ On the number of roots of an algebraic equation contained between given limits, by C. Hermite ’

B. D.O. Anderson^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Hermite’s paper contains an unproved claim that the signature of a bézoutian-like form formed using derivatives of a homogenized prescribed polynomial is equal to the number of real zeros of the polynomial less one. This note proves the result, correcting in the process what appears to be a sign error in its statement.

Original language	English
Pages (from-to)	975-977
Number of pages	3
Journal	International Journal of Control
Volume	27
Issue number	6
DOIs	https://doi.org/10.1080/00207177808922427
Publication status	Published - Jun 1978
Externally published	Yes

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10.1080/00207177808922427

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AB - Hermite’s paper contains an unproved claim that the signature of a bézoutian-like form formed using derivatives of a homogenized prescribed polynomial is equal to the number of real zeros of the polynomial less one. This note proves the result, correcting in the process what appears to be a sign error in its statement.

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Comments on ‘ On the number of roots of an algebraic equation contained between given limits, by C. Hermite ’

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