Derivatives of x^n(x - 1)(x - a) with Rational Roots

  • Paul David Lee Department of Mathematics and Statistics, University of British Columbia Okanagan
  • Blair Kenneth Spearman Department of Mathematics and Statistics, University of British Columbia Okanagan

Abstract

Let n >= 3 denote an integer and a != 0, 1 denote a rational number. For the family of polynomials f (x) = x^n(x - 1)(x - a) with ï¬xed value of n, we show that there exist inï¬nitely many values of a such that the ï¬rst two derivatives of f (x) have rational roots. We ï¬nd two examples of n and a for which the ï¬rst three derivatives of f (x) have rational roots.

Author Biographies

Paul David Lee, Department of Mathematics and Statistics, University of British Columbia Okanagan
Ph.D student, Department of Mathematics
Blair Kenneth Spearman, Department of Mathematics and Statistics, University of British Columbia Okanagan

Professor, Department of Mathematics

Published
2013-04-24
How to Cite
Lee, P. D., & Spearman, B. K. (2013). Derivatives of x^n(x - 1)(x - a) with Rational Roots. European Journal of Mathematical Sciences, 2(2), 209-214. Retrieved from https://ejmathsci.org/index.php/ejmathsci/article/view/145
Issue
Vol 2 No 2
Section
Articles
Upon acceptance of an article by the journal, the author(s) will be asked to transfer copyright of the article to European Journal of Mathematical Sciences. The Copyright Transfer Agreement, which will be provided by the journal, should be signed by the appropriate person. The transfer of copyright does not take place until the manuscript is accepted for publication. If necessary, authors are responsible for obtaining permissions to reprint previously published figures, tables, and other material.