Cubic Polynomials, Linear Shifts, and Ramanujan Cubics

Abstract

We show that every monic polynomial of degree three with complex coefficients and no repeated roots is either a (vertical and horizontal) translation of $y=x^3$ or can be composed with a linear function to obtain a Ramanujan cubic. As a result, we gain some new insights into the roots of cubic polynomials.

9 pages, bibliography

References in corpus (1)

• On Ramanujan Cubic Polynomials