# 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 ofÂ polynomials f (x) = x^n(x - 1)(x - a) with ï¬xed value of n, we show that there exist inï¬nitely manyÂ values of a such that the ï¬rst two derivatives of f (x) have rational roots. We ï¬nd two examples of nÂ and a for which the ï¬rst three derivatives of f (x) have rational roots.

Published

2013-04-24

How to Cite

*European Journal of Mathematical Sciences*,

*2*(2), 209-214. Retrieved from https://ejmathsci.org/index.php/ejmathsci/article/view/145

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Section

Articles

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