Which quartic polynomials have a hyperbolic antiderivative?
Classical Analysis and ODEs
2019-04-19 v2
Abstract
Every linear, quadratic or cubic polynomial having all real zeros is the derivative of a polynomial having all real zeros. The statement is false for higher degree polynomials. In particular, not every fourth degree polynomial with real zeros is the derivative of a polynomial having all real zeros. We derive a necessary and sufficient condition for a quartic polynomial to be the derivative of a polynomial having all real zeros. This condition is a single quadratic form inequality involving the zeros of the quartic polynomial.
Keywords
Cite
@article{arxiv.1901.08156,
title = {Which quartic polynomials have a hyperbolic antiderivative?},
author = {Rajesh Pereira},
journal= {arXiv preprint arXiv:1901.08156},
year = {2019}
}