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 http://ejmathsci.org/index.php/ejmathsci/article/view/145
Section
Articles