Roots algebraic equations and Clifford algebra (Q1579064)

The author investigates roots of real polynomials inside the real two-dimensional Clifford algebra with generator \(\varepsilon\), \(\varepsilon^2=1\), calling the elements of this algebra hyperbolic. The corresponding numbers of real and hyperbolic roots of a polynomial are calculated. As applications, the intersection of a line with an algebraic plane curve is examined, and some remarks on linear differential equations with constant coefficients are given.