Fundamental Theorem of Algebra

The Fundamental Theorem of Algebra is a cornerstone result in mathematics, stating that every non-constant polynomial equation with complex coefficients has at least one complex root. This theorem underscores the profound connection between algebra and complex analysis, revealing that the complex number system is essential for fully understanding polynomial equations. Its implications extend across diverse mathematical disciplines, influencing fields such as number theory, differential equations, and algebraic geometry. By establishing the existence of roots within the complex plane, the Fundamental Theorem of Algebra fundamentally shapes our understanding of polynomial equations and their solutions in both theoretical and practical contexts.