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On the Location of Zeros of Polynomials

Published online by Cambridge University Press:  20 November 2018

A. Joyal ,
G. Labelle  and
Q.I. Rahman
A. Joyal
Affiliation:
Université de Montréal
G. Labelle
Affiliation:
Université de Montréal
Q.I. Rahman
Affiliation:
Université de Montréal
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The different results proved in this paper do not have very much in common. Since they all deal with the location of the zeros of a polynomial, we have decided to put them in one place. Improving upon a classical result of Cauchy we obtain in § 2 a circle containing all the zeros of a polynomial. In § 3 we obtain an extension of the well known theorem of Enestrőm and Kakeya concerning the zeros of a polynomial whose coefficients are non-negative and monotonie.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 1 , April 1967 , pp. 53 - 63
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Fejér, Il., Über Kreisgebiete, in deneneine Wurzeleiner algebraischen Gleichungliegt, Jahresbericht der deutschen Math. Vereinigling, 26 (1911), pages 114-128.Google Scholar
2. Marden, M., The geometry of the zeros of a polynomial in a complex variable. Math. Surveys No. 3, Amer. Math. Soc, Providence R. I. (1944).Google Scholar
3. Rubinstein, Z., Some results in the location of the zeros of linear combinations of polynomials. Transactions of the American Mathematica. Society, 116 (1966) pages 1-8.Google Scholar
4. Szegö, G., Bemerkungen zue inem Satz von Grace, J. H. ûber die Wurzeln algebraischer Gleichungen. Math. Zeitschrift, 1. (1922), pages 28-55.CrossRefGoogle Scholar
5. Zedek, M., Continuity and location of zeros of linear combinations of polynomials. Proc. Amer. Math. Soc, 16 (1966), pages 78-84.CrossRefGoogle Scholar