Cubic Equation Calculator
Solve third-degree polynomial equations (ax³ + bx² + cx + d = 0) for all three roots, including real and complex. Uses Cardano's method and the trigonometric method to handle every possible root configuration.
Enter the four coefficients: a (for x³, must be non-zero), b (for x²), c (for x), and d (the constant). The calculator finds all three roots — which may be three real roots, one real and two complex conjugates, or repeated roots.
Every cubic with real coefficients has exactly three roots (counting multiplicity). If the discriminant Δ > 0: three distinct real roots. Δ = 0: at least two roots are equal. Δ < 0: one real root and two complex conjugate roots. The calculator uses the trigonometric method when all three roots are real to avoid the casus irreducibilis problem with Cardano's formula.
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