# On the discriminant of a certain quartinomial and its totally complexness

Otake, Shuichi and Shaska, Tanush (2018) On the discriminant of a certain quartinomial and its totally complexness. Algebraic Curves. pp. 1-20. (Unpublished)

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On the discriminant of a certain quartinomial and its totally complexness.pdf - Draft Version

In this paper, we compute the discriminant of a quartinomial of the form $f_{(b,a,1)}(t; x)=x^n+t(x^2+ax+b)$ by using the Bezoutian. Then, by using this result and another theorem of our previous paper, we construct a family of totally complex polynomials of the form $f_{(b,a,1)}(\xi, x)$ $(\xi \in \R, \left(a, b)\neq (0,0)\right)$.