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