Roots of Polynomials

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


In all we have done so far concerning polynomials, at no moment we had any intent of substituting X by an element of \(\mathbb K\). Even in Theorem  14.10 and Example  14.15, the notation f(z), used to denote the complex number obtained by formally substituting X by z in the expression of \(f\in \mathbb C[X]\), was a mere convention. This is no surprise, for we are looking at polynomials as formal expressions, rather than as functions. In this sense, the indeterminate X is a symbol with no arithmetic meaning, and we have even stressed before that we could have used the symbol \(\square \), instead.


  1. 9.
    A. Caminha, An Excursion Through Elementary Mathematics II - Euclidean Geometry (Springer, New York, 2018)Google Scholar
  2. 20.
    C.R. Hadlock, Field Theory and its Classical Problems (Washington, MAA, 2000)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

Personalised recommendations