Quadratic Equation over Associative D-Algebra

Abstract

In this paper, I treat quadratic equation over associative $D$-algebra. In quaternion algebra $H$, the equation $x^2=a$ has either $2$ roots, or infinitely many roots. Since $a\in R$, $a<0$, then the equation has infinitely many roots. Otherwise, the equation has roots $x_1$, $x_2$, $x_2=-x_1$. 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.

English text - 38 pages; Russian text - 39 pages

References in corpus (4)

• Solution of a quadratic quaternion equation with mixed coefficients
• Linear Map of $D$-Algebra
• Polynomial over Associative D-Algebra
• Introduction into Calculus over Banach algebra

Cited by in corpus (1)

• Differential Equation over Banach Algebra