GENERATING INFINITE FAMILIES OF MONOGENIC POLYNOMIALS USING A NEW DISCRIMINANT FORMULA.

Recently, Otake and Shaska have given a formula for the discrim- inant of quadrinomials of the form f(x) = xn + t(x² + ax + b). In their concluding remarks, they ask if a formula can be found for the discriminant of f(x) = xn + tg(x) when n > deg(g) = 3. Assuming that f(x) = xn + tg(x) is irreducible, and under certain restrictions on a polynomial related to g(x), in this article we give a formula for the discriminant of f(x), regardless of deg(g) ≥ 1. We then use our discriminant formula to generate some new in- finite families of monogenic polynomials f(x) = xn + tg(x) with n > deg(g), when g(x) is monic and deg(g) ∊ {2; 3; 4}. [ABSTRACT FROM AUTHOR]