本项目以判别式理论为工具，研究多项式方程根的构型问题。首先将经典判别式推广，构造多项式方程的高阶判别式和包含根重数信息的判别式；然后探索这些判别式和多项式方程根的构型之间的内在关系，从而在无需精确计算出多项式根的情况下，准确获知根的分布情况。本项目拟建立一个完整的研究广义判别式的理论框架，为高次方程根的构型问题研究提供切实可行的理论依据与算法支持。

The project will employ the discriminant theory to investigate the root configurations of polynomial equations. We first generalize the classical discriminant and construct the high-order discriminant and discriminants which contain the multiplicity information of roots. Then the interior relationship between these discriminants and the root configuration of polynomials is explored so that one can acquire the exact root distributions without calculating the exact roots. The project will establish a complete theoretical framework for studying generalized discriminants and provide a practical theoretical and algorithmic support for solving root configuration problem of polynomial equations with higher degree.