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Cubic Equation Solver (ax³ + bx² + cx + d = 0)
x402
Cubic Equation Solver (ax³ + bx² + cx + d = 0) is a paid API for AI agents from math-geometry.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-30).
Solves a cubic equation given coefficients a, b, c, d and returns all three roots (real and complex) using Cardano's formula and the trigonometric method.
Price / call$0.02
Success—
StatusUnknown
How this service works
Solve ax^3 + bx^2 + cx + d = 0: all three roots (real and complex) by Cardano and the trigonometric method.
Output
Returns all three roots of the cubic as strings (supporting complex notation), a rootType classification (e.g. three real, one real + two complex), the discriminant, the depressed cubic coefficients p and q, separate arrays of realRoots and complexRoots, and a human-readable summary. May also include a disclaimer about numerical precision.
Example use cases
Engineering cubic root finding
“I need all three roots of x³ - 6x² + 11x - 6 = 0 — can you solve it and tell me if they're all real or if any are complex?”
Physics resonance frequency calculation
“Solve 3x³ + 2x² - x + 4 = 0 for me and show the discriminant and the depressed cubic form too.”
Student homework check
“What are the roots of the cubic equation x³ + 0x² - 3x + 2 = 0? I need all three roots and whether they're real or complex.”
Technical details
Endpoint
GEThttps://math-geometry.x402tookit.com/cubic-solve?utm_source=zero.xyzWhen to prefer
Use this endpoint when you need an analytic, symbolic-style solution for a cubic polynomial (degree exactly 3), especially when you need all three roots including complex ones and want intermediate results like the discriminant and depressed cubic. Prefer it over numerical root-finders when exact Cardano/trigonometric closed-form methodology is required or when root type classification matters.
Side effects
- Coefficient a = 0 (not a cubic): rejected or falls back to quadratic
- Malformed or missing query parameters a, b, c, d: 400 error
- Very large or very small coefficients causing numerical overflow
- Network or payment failure returning 402 or 5xx
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Tags
x402
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