THEORETICAL FOUNDATIONS AND PRACTICAL APPLICATIONS OF BÉZOUT’S THEOREM IN ALGEBRA AND PARAMETRIC POLYNOMIAL ANALYSIS
Keywords:
Keywords: Bézout’s theorem, polynomial division, roots of polynomials, algebraic equations, François Bézout, parametric polynomials, root multiplicity, applied mathematics, system optimization.Abstract
Annotation: This thesis explores Bézout’s theorem, which connects polynomial division and root identification, emphasizing its theoretical foundations and historical significance through François Bézout’s contributions. Practical examples demonstrate the theorem’s applications in solving equations, analyzing parametric polynomials, and optimizing parameters in research. The relevance of Bézout’s theorem is highlighted in modern studies of algebraic structures and its applications in science and engineering.
References
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