# Quadratics — Randomly

> Integer, rational or surd roots — built from the roots, so they factor. One of 63 generators at [Randomly](https://randomly.cluxnei.dev), a library of random generators seeded from verifiable real-world entropy. Free HTTP API, no key, no signup.

## `equations.quadratic` — Quadratics

Integer, rational or surd roots — built from the roots, so they factor.

| | |
|---|---|
| **Key** | `equations.quadratic` |
| **Module** | `equations` |
| **Version** | `1` — a permalink carries this, and a replay against a different version returns `409` rather than something else |
| **Formats** | `application/json`, `text/plain` |
| **Studio** | https://randomly.cluxnei.dev/g/equations/quadratic |
| **API** | `GET https://randomly.cluxnei.dev/api/v1/g/equations.quadratic` |

`value.problems` is a list of problems with their answers; `meta.latex` carries the same in LaTeX.

| Parameter | Type | Default | Accepts | What it does |
|---|---|---|---|---|
| `roots` | enum | `integer` | `integer`, `rational`, `surd`, `mixed` | Root type |
| `monic` | bool | `false` | `true`, `false` | Leading coefficient 1 — Off lets the x² term carry a coefficient. |
| `count` | int | `6` | `1` – `50` | How many |

Out-of-range numbers are **clamped, not rejected**, so a request never fails for being
ambitious — but it may not do what you meant. Unknown keys are dropped and missing ones
fall back to the defaults above.

```bash
curl -s 'https://randomly.cluxnei.dev/api/v1/g/equations.quadratic?roots=integer&monic=0&count=6' -H 'Accept: text/plain'
```

## The receipt

Every result carries one, naming the physical source of the randomness and linking to the
third party's own record of it:

```json
"receipt": {
  "source": "seismic",
  "source_label": "USGS Seismic Feed",
  "class": "C",
  "caveat": "Carries only tens of bits of genuine surprise. Always mixed with the OS CSPRNG.",
  "narrative": "A magnitude 3.6 earthquake, 67 km N of Culebra, Puerto Rico, 39.6 km down — 52 minutes ago.",
  "proof_url": "https://earthquake.usgs.gov/earthquakes/eventpage/us7000th33",
  "mixed_with_csprng": true,
  "degraded": false
}
```

Pick the source with `?source=`, or leave it at the default `auto`:

- **Class A** (Cryptographic) — `csprng`, `anu-qrng`, `random-org`
- **Class B** (Public beacon) — `nist-beacon`, `drand`, `bitcoin`. Published openly — anyone can look this value up after the fact.
- **Class C** (Observational) — `seismic`, `space-weather`, `atmosphere`, `iss`. Carries only tens of bits of genuine surprise. Always mixed with the OS CSPRNG.

## More

- [The full API contract](https://randomly.cluxnei.dev/api.md)
- [Everything in one file](https://randomly.cluxnei.dev/llms-full.txt)
- [The catalogue as JSON](https://randomly.cluxnei.dev/api/v1/generators)
- [This generator in the browser](https://randomly.cluxnei.dev/g/equations/quadratic)