The Zeros of Quadratic Coquaternionic Polynomials Revisited

In this paper, we address the problem of solving the quadratic equation x(2) + bx + c = 0, where b and c are elements of the algebra of coquaternions. The nature of this algebra leads, as expected, to results very different from the ones obtained in the classical complex case, making the root-finding problem much more demanding. In this paper we derive straightforward conditions to characterize the number and form of the non-isolated zeros of monic quadratic coquaternionic equations. Through carefully constructed examples and by leveraging the Mathematica system, we illustrate the core findings and showcase the array of scenarios that may emerge.