Discriminants of special quadrinomials

Abstract

Finding an effective formula for describing a discriminant of a quadrinomial (a formula which can be easily computed for high values of degrees of quadrinomials) is a difficult problem. In 2018 Otake and Shaska using advanced matrix operations found an explicit expression of $\Delta (x^n+t(x^2+ax+b))$. In this paper we focus on deriving similar results, taking advantage of alternative elementary approach, for quadrinomials of the form $x^n+a{x}^k+bx+c$, where $k\in \{2,3,n-1\}$. Moreover, we make some notes about $\Delta (x^{2n}+a{x}^n+b{x}^l+c)$ such that $n>2l$.

arXiv comment15 pages