# Quadratic Equation Solver

> 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.

## Facts

- Endpoint: GET https://math-geometry.x402tookit.com/quadratic-solve?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-11-03
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/quadratic-equation-solver-0a6d0861
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_l0RiHMwNf7kkqJNSikZ31

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability quadratic-equation-solver-0a6d0861
```

Example prompt: Can you solve the quadratic equation 2x² - 4x - 6 = 0? I need the roots, discriminant, vertex, axis of symmetry, and factored form.

## When to prefer this

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.

## Known failure modes

- 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

## 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.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method"
   ],
   "properties": {
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "GET"
     ],
     "type": "string"
    },
    "queryParams": {
     "type": "object",
     "required": [
      "a",
      "b",
      "c"
     ],
     "properties": {
      "a": {
       "type": "number",
       "description": "Coefficient of x^2 (not 0)"
      },
      "b": {
       "type": "number",
       "description": "Coefficient of x"
      },
      "c": {
       "type": "number",
       "description": "Constant term"
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object",
     "properties": {
      "a": {
       "type": [
        "null",
        "number"
       ]
      },
      "b": {
       "type": [
        "null",
        "number"
       ]
      },
      "c": {
       "type": [
        "null",
        "number"
       ]
      },
      "asOf": {
       "type": [
        "null",
        "string"
       ]
      },
      "roots": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "number"
       }
      },
      "source": {
       "type": [
        "null",
        "string"
       ]
      },
      "vertex": {
       "type": [
        "null",
        "object"
       ],
       "properties": {
        "x": {
         "type": [
          "null",
          "number"
         ]
        },
        "y": {
         "type": [
          "null",
          "number"
         ]
        }
       }
      },
      "reasons": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "summary": {
       "type": [
        "null",
        "string"
       ]
      },
      "verdict": {
       "type": [
        "null",
        "string"
       ]
      },
      "degraded": {
       "type": [
        "boolean",
        "null"
       ]
      },
      "factored": {
       "type": [
        "null",
        "string"
       ]
      },
      "rootType": {
       "type": [
        "null",
        "string"
       ]
      },
      "disclaimer": {
       "type": [
        "null
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/quadratic-equation-solver-0a6d0861/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from math-geometry.x402tookit.com](https://www.zero.xyz/host/math-geometry.x402tookit.com/llms.txt)