THE DEVELOPMENT OF THE THEORY OF ALGEBRAIC EQUATIONS IN THE SIXTEENTH AND SEVENTEENTH CENTURIES: AN ANALYSIS OF THE METHODS OF CARDANO, TARTAGLIA, AND BOMBELLI

Uralova Ruxshona Alijon kizi,Bozarov Dilmurod Uralovich

Authors

Uralova Ruxshona Alijon kizi,Bozarov Dilmurod Uralovich Second-year student of Mathematics, University of Economics and Pedagogy,Acting Associate Professor, Department of Mathematics University of Economics and Pedagogy

Keywords:

algebraic equation, cubic equation, Cardano’s formula, Tartaglia’s method, Bombelli, Ferrari, complex numbers, history of mathematics, mathematics of the sixteenth and seventeenth centuries.

Abstract

This article analyzes the formation and development of the theory of algebraic equations in the sixteenth and seventeenth centuries from a historical and mathematical point of view. The main focus is placed on the problem of solving cubic and quartic equations, particularly on the rise of algebraic thinking to a new stage through the works of Tartaglia, Cardano, Ferrari, and Bombelli. The article discusses the reduction of a cubic equation to its depressed form, Cardano’s formula, discriminant cases, the historical necessity of complex numbers, and the mathematical significance of Bombelli’s approach. In addition, the methodological importance of the history of algebraic solutions in higher mathematics education is demonstrated. In the practical section, several examples related to cubic equations are solved step by step, and a modern interpretation of historical formulas is presented. The results of the study show that the methods for solving algebraic equations developed in the sixteenth and seventeenth centuries had a strong influence not only on the development of algebra, but also on the subsequent progress of mathematical analysis, number theory, and the theory of complex numbers.

References

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