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Cubic Equation Calculator

Solve Cubic Equation

Find all roots of ax³ + bx² + cx + d = 0

Formula

Depressed: t³ + pt + q = 0 | x = t - b/(3a) | Cardano: t = ∛(-q/2 + √D) + ∛(-q/2 - √D)

Frequently Asked Questions

How many roots does a cubic equation have?
A cubic equation always has exactly 3 roots (counting multiplicity). These can be: 3 distinct real roots, 1 real + 2 complex conjugate roots, or roots with multiplicity (e.g., a triple root or a single + double root).
What is the cubic formula?
The cubic formula (Cardano's formula) solves t³ + pt + q = 0 by: t = ∛(-q/2 + √(q²/4 + p³/27)) + ∛(-q/2 - √(q²/4 + p³/27)). First convert ax³+bx²+cx+d=0 to depressed form by substituting x = t - b/(3a).

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