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Quadratic Equation Solver
x402
Quadratic Equation Solver is a paid API for AI agents from math-geometry.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-11-03).
Solves ax² + bx + c = 0 and returns real or complex roots, discriminant, vertex, axis of symmetry, factored form, and other properties.
Price / call$0.02
Success—
StatusUnknown
How this service works
Solve ax^2 + bx + c = 0: real or complex roots, discriminant, vertex, axis of symmetry and factored form.
Output
Returns the three original coefficients (a, b, c), the discriminant value, root type (real/complex/repeated), the roots array, vertex coordinates (x, y), axis of symmetry equation, factored form string, sum and product of roots, y-intercept, whether the parabola opens upward, a human-readable summary, and optional degraded/disclaimer flags.
Example use cases
Checking student homework answers
“My student wrote that the roots of x² - 5x + 6 = 0 are x=2 and x=3. Can you solve it properly and show me the discriminant, factored form, and vertex so I can verify their work?”
Finding parabola vertex for graphing
“I need to graph the parabola 3x² + 12x + 9 = 0 — can you find the vertex, axis of symmetry, and whether it opens upward or downward?”
Engineering equation with complex roots
“Solve the quadratic equation x² + 2x + 5 = 0 for me — I'm expecting complex roots, so show me all the details including the discriminant and factored form.”
Technical details
Endpoint
GEThttps://math-geometry.x402tookit.com/quadratic-solve?utm_source=zero.xyzWhen to prefer
Choose this endpoint when you need a full algebraic analysis of a single quadratic (degree-2 polynomial) including roots, vertex, discriminant, and factored form in one call. Prefer the cubic solver sibling for degree-3 polynomials or the linear system solver for multi-variable linear equations.
Side effects
- Coefficient a = 0 makes it not a quadratic — request likely rejected or undefined behavior
- Non-numeric or missing a, b, or c parameters return an error
- Very large or very small coefficients may cause floating-point precision issues in roots
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Tags
x402
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