LINEAR AND QUADRATIC EQUATIONS IN NON-STANDARD FORM
Keywords:
Keywords: non-standard equation, linear equation, quadratic equation, parameter, modular, fractional-rational equation, irrational equation, method, discriminant, Vieta's theorem, domain of determination, equivalent constant.Abstract
Abstract
This article studies the non-standard design of linear and quadratic equations,
their simplification using algebraic methods, and effective methods for solving them.
Non-standard equations can have modular, fractional-rational expressions, roots, or
hidden quadratic structures. In such problems, it is necessary to understand the internal
structure of the equation, correctly determine the domain of determination, correctly
collect the equivalent domains, and raise the found roots in a new equation. The article
analyzes modular, fractional, root, and parametric equations using examples of solving
them and methods for reducing them to a quadratic equation.
References
References:
1. Abdukhamidov A. U., Nasimov H. A., Nosirov U. M., Khusanov J. H.
Fundamentals of Algebra and Mathematical Analysis. – Tashkent: O’qituvati, 2014. –
400 p.
2. Nazarov R. N., Toshpu’latov B. T., D’osumbetov A. D. Algebra and Number
Theory. – Tashkent: O’qituvati, 1993.
3. Ayupov Sh. A., Omirov B. A., Khudoyberdiev A. Kh. et al. Linear Algebra.
– Tashkent: Muxr-Press, 2023. – 392 p.
4. Alimov Sh. A., Kholmukhamedov M. A., Mirzaahmedov M. A. Algebra: a
textbook for general secondary schools. – Tashkent: O’qituvati.
5. Mirzaahmedov M. A. et al. Fundamentals of algebra and analysis. Textbook
for academic lyceums. – Tashkent: Teacher.
6. Ayupov Sh. A. et al. Collection of problems on algebra and number theory. –
Tashkent: Science.
7. Stewart J. Algebra and trigonometry. – Boston: Cengage Learning.
8. Sullivan M. Algebra and trigonometry. – Boston: Pearson.
9. Polya G. How to solve mathematics. – Princeton: Princeton University Press,
1945.
10. Bronshteyn I. N., Semendyayev K. A. Handbook of mathematics. – Moscow:
Nauka.
11. Vilenkin N. Ya. Elements of algebra and mathematical analysis. – Moscow:
Prosveshchenie.
12. Abdukodirov A. A. Mathematics teaching methodology. – Tashkent:
Teacher.
