August 2024
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Italian Journal of Pure and Applied Mathematics
In this paper, we present some numerical applications for the equation x 2 + ax + b = 0, where a, b are two quaternionic elements in H(α, β). H(α, β) represents the algebra of real quaternions with parameterized coefficients by α and β. The algebra of real quaternions is an extension of complex numbers and is represented by algebraic objects called quaternions. These quaternions are composed of four components: a real part and three imaginary components. In general, H(α, β) indicates a family of parameterized quaternion algebras, in which the specific values of α and β determine the specific properties and structure of the quaternion algebra. 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 H(α, β).