一元二次四元数单边多项式的求根公式

随着四元数代数广泛应用于量子力学、惯性导航及控制论等学科，四元数多项式的求根问题被许多学者关注。最近Janovska和Opfer从理论上给出了一种n次四元数单边多项式零点的求解方法，Feng和Zhao进一步给出了一般n次四元数单边多项式的零点显性表达式。 本文根据Feng和Zhao的结果对一元二次四元数单边方程的根进行了讨论，并利用复数域上四次多项式的Ferrari求根公式建立了一元二次四元数单边方程的求解公式。与文献中现有的结果相比，本文建立的求根公式在许多方面展现了优越性。

Formulae for Finding All Roots of Quadratic One-sided Polynomials over Quaternions

Quaternion algebra has been widely applied to many subjects such as quantum mechanics, control theory and inertial navigation. With this it has been paid attentions by many scholars to effectively obtain the roots of a quaternionic polynomial. Recently, Janovska and Opfer have provided theoretically a method of finding all zeros of a simple quaternionic polynomial of degree n. Furthermore, Feng and Zhao have given a formula of finding all zeros of a general simple quaternionic polynomial of degree n in terms of solving polynomials over the field of complex numbers. Basing on the results given by Feng and Zhao, in this paper, we discuss and classify the roots of a quaternionic one-sided polynomial with degree 2, and produce a quadratic formula for quaternions by help of the Ferrari's quartic formula over the field of complex numbers. Comparing with the results in literature, the formula we built in this paper presents its advantages in many aspects.