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A Separation Method of the Positivity of A Quartic Polynomial

Taehun Kim, Jung Chan Lee, ByoungSeon Choi

Abstract

Although the positivity of a quartic polynomial is a well-researched topic, existing conditions are often highly complex. Some necessary and sufficient conditions for the positivity of a quartic polynomial are presented through a separation method based on Ferrari's technique of solving a quartic equation. We apply the result to the problem of the projection of the coefficient space.

A Separation Method of the Positivity of A Quartic Polynomial

Abstract

Although the positivity of a quartic polynomial is a well-researched topic, existing conditions are often highly complex. Some necessary and sufficient conditions for the positivity of a quartic polynomial are presented through a separation method based on Ferrari's technique of solving a quartic equation. We apply the result to the problem of the projection of the coefficient space.
Paper Structure (1 section, 1 theorem, 30 equations, 1 figure)

This paper contains 1 section, 1 theorem, 30 equations, 1 figure.

Table of Contents

  1. Application

Key Result

Theorem 1

The Followings Are Equivalent:

Figures (1)

  • Figure 1: Two functions $h_m(x)$ and $g_m(x)$, and the separation line.

Theorems & Definitions (2)

  • Theorem
  • proof