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2 results

  • Zero-Free Regions for Polynomials and Some Generalizations of Eneström-Kakeya Theorem

  • Abdul Aziz, Q. G. Mohammad
  • Journal:
    Canadian Mathematical Bulletin / Volume 27 / Issue 3 / 01 September 1984
    Published online by Cambridge University Press:
    20 November 2018, pp. 265-272
    Print publication:
    01 September 1984
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  • In this paper we shall use matrix methods to obtain several generalizations of a well known result of Eneström and Kakeya about the location of the zeros of polynomials. We shall also obtain zero-free regions of polynomials having complex coefficients. Finally we prove some results concerning the zeros of a class of polynomials.

  • Remark on Irreducible Factorizations of Polynomials in Several Variables*

  • Leiba Rodman
  • Journal:
    Canadian Mathematical Bulletin / Volume 24 / Issue 4 / 01 December 1981
    Published online by Cambridge University Press:
    20 November 2018, pp. 493-496
    Print publication:
    01 December 1981
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  • It is proved that a polynomial on several complex variables, whose coefficients depend analytically on a parameter ε, admits a factorization which is irreducible for every value of the parameter, with the possible exception of an analytic set of points. Moreover, the coefficients of the irreducible factors can be chosen to depend analytically on ε in a neighborhood of every point not belonging to this analytic set.