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