Some fixed points results of quadratic functions in split quaternions (Q324651)

Summary: We attempt to find fixed points of a general quadratic polynomial in the algebra of split quaternions. In some cases, we characterize fixed points in terms of the coefficients of these polynomials and also give the cardinality of these points. As a consequence, we give some simple examples to strengthen the infinitude of these points in these cases. We also find the roots of quadratic polynomials as simple consequences.