Discriminants of special quadrinomials

Abstract

Finding an effective formula for describing the 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 for $\mathrm{\Delta }(x^n+t(x^2+ax+b))$. In this paper, we focus on deriving similar results, taking advantage of an 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 $\mathrm{\Delta }(x^{2n}+a{x}^n+b{x}^l+c)$, where .