This article provides a comprehensive analysis of quadratic equations and their practical applications in various fields. The quadratic equation is one of the most fundamental and widely used equations in mathematics, applied not only in theoretical sciences but also in everyday life, technology, economics, engineering, physics, and other areas. The study covers the general form of a quadratic equation, methods for finding its solutions, the concept of the discriminant, and the use of formulas to determine roots. Practical examples include applications in construction calculations, financial forecasting, mechanics, and electronic device design. The research also evaluates the effectiveness of traditional algebraic solution methods alongside graphical and digital approaches. Moreover, the pedagogical significance of applying quadratic equations in education is highlighted, emphasizing the development of logical thinking and problem-solving skills in students. This study contributes to linking mathematical knowledge with real-world problems and promotes interdisciplinary integration.

quadratic equation, discriminant, solution, practical application, graphical method, digital computation, mathematics, problem-solving

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