A new method for roots of monic quaternionic quadratic polynomial

The purpose of this paper is to show how the problem of finding roots (or zeros) of the monic quaternionic quadratic polynomials (MQQP) can be solved by its equivalent real quadratic form. The real quadratic form matrices, firstly defined in this paper, are used to form a simple equivalent real quadratic form of MQQP. Some necessary and sufficient conditions for the existence of roots of MQQP are also presented. The main idea of the practical method proposed in this work can be summarized in two steps: translating MQQP into its equivalent real quadratic form, and giving directly the quaternionic roots of MQQP by solving its equivalent real quadratic form.