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

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 $\mathbb{H}(\alpha ,\beta )$.