Interactive Cubic Formula Demo

This GeoGebra applet dynamically demonstrates the complete solution process of the cubic equation ax³+bx²+cx+d=0 using Cardano's formula. Core mathematical concepts include: roots of cubic polynomials, the relationship between discriminant Δ and root nature (three real roots or one real with two complex conjugate roots), and geometric interpretation of complex roots. Construction highlights: If command for conditional branches based on discriminant, Unique command to ensure root uniqueness, LaTeX command for real-time formula rendering; sliders to adjust coefficients a₀, a₁, a₂ and observe root variations and function graph intersections; visualization of complex roots z₁, z₂, z₃ on the complex plane. Suitable for high school elective mathematics or college-preparatory algebra courses, helping students understand algebraic methods and geometric intuition for solving higher-degree equations.