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Polynomials Over \(\boldsymbol {\mathbb R}\)

  • Antonio Caminha Muniz Neto
Chapter
Part of the Problem Books in Mathematics book series (PBM)

Abstract

This chapter revisits, for real polynomials and departing from the fundamental theorem of Algebra, some classical theorems of Calculus. As applications of them, we shall prove Newton’s inequalities, which generalizes the classical inequality between the arithmetic and geometric means of n positive real numbers, and Descartes’ rule, which relates the number of positive roots of a real polynomial with the number of changes of sign in the sequence of its nonzero coefficients.

References

  1. 3.
    T. Apostol, Calculus, Vol. 1 (Wiley, New York, 1967)Google Scholar
  2. 8.
    A. Caminha, An Excursion Through Elementary Mathematics I - Real Numbers and Functions (Springer, New York, 2017)Google Scholar
  3. 26.
    A.G. Kurosch, Curso de Algebra Superior (in Spanish) (MIR, Moscow, 1968)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Antonio Caminha Muniz Neto
    • 1
  1. 1.Universidade Federal do CearáFortalezaBrazil

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