Roots of Second Order Polynomials with Real Coefficients in Elliptic Scator Algebra

Abstract

The roots of second order polynomials with real coefficients are obtained in the S 1+2 scator set. Explicit formulae are computed in terms of the polynomial coefficients. Although the scator product does not distribute over addition, the lack of distributivity is surmountable in order to find the zeros of the polynomial. The structure of the solutions and their distribution in 1+2 dimensional scator space are illustrated and discussed. There exist six, two, or eight solutions, depending on the value of polynomial coefficients. Four of these roots only exist in the hypercomplex S 1+2 \ S 1+1 set.