# Quadratic Formula Calculator (x402.forgemesh.io)

> Quadratic Formula Calculator (x402.forgemesh.io) is a paid API for AI agents from x402.forgemesh.io, paid per call via x402, $0.002/call, status unknown (last checked 2026-09-15).

Solves quadratic equations (ax²+bx+c=0), linear equations, and 2x2 linear systems, returning exact real or complex roots and the discriminant.

## Facts

- Endpoint: POST https://x402.forgemesh.io/quadratic-formula-calculator
- Price: $0.002/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/quadratic-formula-calculator-x402-forgemesh-io-b04ceee9
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_wdNQ9VG9KNDXsi3s5DIix

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-formula-calculator-x402-forgemesh-io-b04ceee9 -d '<json body>'
```

Example prompt: Solve the quadratic equation 2x² + 3x - 5 = 0 for me and give me both roots along with the discriminant — I need the exact values, not a decimal approximation.

## When to prefer this

Choose this endpoint when you need exact algebraic roots (including complex numbers) of a quadratic, linear equation, or 2x2 system rather than numerical approximation. Particularly useful for homework verification, engineering calculations, and any workflow requiring discriminant values or symbolic-quality precision at low cost ($0.002/call).

## Known failure modes

- Missing required coefficient fields returns a validation error
- Non-numeric coefficient strings cause a parsing error
- Unrecognized 'type' enum value (not 'linear', 'quadratic', or 'system2') returns an error
- Incomplete 2x2 system parameters (missing a1/a2/b1/b2/c1/c2) causes a failure
- Payment not provided or insufficient USDC results in HTTP 402

## How this service works

Solves quadratic equations (ax squared + bx + c = 0) from numeric coefficients, returning both roots — real or complex — along with the discriminant. Also handles linear equations and small 2x2 systems. For algebra homework checking, engineering calculations, and any agent that needs exact roots instead of an approximated answer.

## Output

Returns both roots (real or complex) of the specified equation, the discriminant value, and relevant classification of the solution (e.g. two distinct real roots, repeated root, complex conjugate pair).

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "a": {
   "type": "string"
  },
  "b": {
   "type": "string"
  },
  "c": {
   "type": "string"
  },
  "a1": {
   "type": "string"
  },
  "a2": {
   "type": "string"
  },
  "b1": {
   "type": "string"
  },
  "b2": {
   "type": "string"
  },
  "c1": {
   "type": "string"
  },
  "c2": {
   "type": "string"
  },
  "type": {
   "type": "string",
   "description": "linear | quadratic | system2"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "json",
 "example": {
  "roots": [
   2,
   1
  ],
  "nature": "two real roots",
  "discriminant": 1
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/quadratic-formula-calculator-x402-forgemesh-io-b04ceee9/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from x402.forgemesh.io](https://www.zero.xyz/host/x402.forgemesh.io/llms.txt)