2015/05/30 by Aleks Kleyn, Kleyn, Aleks
Computer Science · Mathematics · #Matrix Theory and Algorithms #Algebraic and Geometric Analysis #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.1506.00061
In this paper, I treat quadratic equation over associative D-algebra. In quaternion algebra H, the equation x2=a has either 2 roots, or infinitely many roots. Since a∈ R, a<0, then the equation has infinitely many roots. Otherwise, the equation has roots x1, x2, x2=-x1. I considered different forms of the Viete's theorem and a possibility to apply the method of completing the square. In quaternion algebra, there exists quadratic equation which either has 1 root, or has no roots.