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[3] viXra:2506.0104 [pdf] replaced on 2025-07-09 11:41:42
Authors: Timothy Jones
Comments: 4 Pages. Added more complete TI84-CE program.
The Euclidean Algorithm finds the greatest common divisor (GCD) of two integers; it also gives a way to express the GCD as an integer linear combination of the two numbers. This latter feature is not easily done by hand. We present programs for the Euclidean Algorithm and give a fast and easy way to find this linear combination.
Category: Algebra
[2] viXra:2506.0089 [pdf] submitted on 2025-06-17 20:22:05
Authors: Yingxin Dai
Comments: 5 Pages.
This paper explores the role of the discriminant in solving quadratic equations. Using the quadratic formula, we can determine whether a quadratic equation has real roots, how many it has, and whether those roots are rational or irrational. Several examples and graphs are provided to illustrate how the value of the discriminant affects the number of real roots and the position of the parabola on the coordinate plane. Real-life applications, such as motion under gravity and the intersection of lines and circles, are also discussed to enhance understanding.
Category: Algebra
[1] viXra:2506.0008 [pdf] submitted on 2025-06-03 23:38:51
Authors: Marciano L. Legarde
Comments: 3 Pages. (Note by viXra Admin: Please remove strange word!)
This paper introduces and formalizes the Theoxist Coefficient Shortcut Method, an intuitive shortcut for solving a specific class of quadratic equations of the form (ax)^2 = bx. The method allows for quick identification of solutions using proportional reasoning. We outline the method, prove its validity, provide examples, and discuss its educational significance within the broader context of algebraic problem-solving strategies.
Category: Algebra
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