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.

翻译：尽管四次多项式的正定性是一个研究充分的课题，但现有条件往往高度复杂。基于费拉里求解四次方程的方法，通过一种分离技巧，本文给出了四次多项式正定性的一些充要条件。并将该结果应用于系数空间的投影问题。