Quadratic split quaternion polynomials factorize exactly under conditions that can be read off from intersections with the null quadric, and every such polynomial with linearly independent coefficients or vanishing norm admits a factorization.
Quadratic formulas for generalized quaternions
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Quadratic Split Quaternion Polynomials: Factorization and Geometry
Quadratic split quaternion polynomials factorize exactly under conditions that can be read off from intersections with the null quadric, and every such polynomial with linearly independent coefficients or vanishing norm admits a factorization.