A Method for Solving quadratic Equations in Real Quaternion Algebra by using Scilab software

Abstract

In this paper, we present some numerical applications for the equation $x^2+ax+b=0$, where $a,b$ are two quaternionic elements in $\mathbb{H}(\alpha ,\beta )$. Based on well-known solving methods, we have developed a new numerical algorithm that solves the equation for any quaternions a and b in any algebra $\mathbb{H}(\alpha ,\beta )$.

In this article, we have provided an algorithm in Scilab which allows us to find solutions for the monic quadratic equation $x^2+bx+c=0$, with $b,c\in \mathbb{H}(\alpha ,\beta )$. By feeding the algorithm with the quaternions b and c and using the formulas, we compute A, B, and C, determine the case, and find the two solutions of the monic quadratic equation