Cubic Solve

{
  "a": 1,
  "asOf": "2026-10-11T08:51:18.592Z",
  "b": -6,
  "c": 11,
  "complexRoots": [],
  "d": -6,
  "degraded": false,
  "depressed": {
    "discriminant": -0.03703703704,
    "p": -1,
    "q": 0
  },
  "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
  "notChecked": [
    "exact radical forms (results are decimals)",
    "accuracy for extreme coefficient ratios beyond double precision"
  ],
  "realRoots": [
    1,
    2
  ],
  "reasons": [
    "Reduced to a depressed cubic t^3 + pt + q = 0; the sign of q^2/4 + p^3/27 selects the method. Real roots are polished with Newton steps.",
    "A cubic always has at least one real root."
  ],
  "rootType": "three distinct real roots",
  "roots": [
    "1",
    "2",
    "…1 more"
  ],
  "source": "computed locally",
  "summary": "1x^3 + -6x^2 + 11x + -6 = 0: 1, 2, 3 (three distinct real roots).",
  "verdict": "THREE_REAL_ROOTS"
}

# bash or zsh: see the payment challenge. Nothing is charged.
curl -sS -g -i 'https://math-geometry.x402tookit.com/cubic-solve?a=1&b=-6&c=11&d=-6'

# x402 v2 sends the challenge base64-encoded in the PAYMENT-REQUIRED header (v1 sends it in the body).
# To read the header:
curl -sS -g -o /dev/null -D - 'https://math-geometry.x402tookit.com/cubic-solve?a=1&b=-6&c=11&d=-6' \
  | grep -i '^payment-required:' | cut -d' ' -f2 | tr -d '\r' | base64 --decode

// npm i @x402/fetch @x402/evm viem
import { wrapFetchWithPayment, x402Client } from "@x402/fetch";
import { registerExactEvmScheme } from "@x402/evm/exact/client";
import { privateKeyToAccount } from "viem/accounts";

// Pays at most $0.02 per call.
const client = new x402Client().setSpendControls({ maxAmountPerPayment: "$0.02" });
registerExactEvmScheme(client, { signer: privateKeyToAccount(process.env.EVM_PRIVATE_KEY) });
const pay = wrapFetchWithPayment(fetch, client);

// Not sure it's safe to pay? ToolVet checks it first for $0.005. Pay for that from a separate
// client: this one is capped at $0.02 per payment. GET https://toolvet.app/api/v1/check?url=https%3A%2F%2Fmath-geometry.x402tookit.com%2Fcubic-solve
const res = await pay("https://math-geometry.x402tookit.com/cubic-solve?a=1&b=-6&c=11&d=-6");
console.log(res.status, await res.text());

# pip install "x402[requests,evm]"
import os
from eth_account import Account
from x402 import x402ClientSync
from x402.http.clients import x402_requests
from x402.mechanisms.evm import EthAccountSigner
from x402.mechanisms.evm.exact.register import register_exact_evm_client

# Pays at most $0.02 per call.
client = x402ClientSync().set_spend_controls({"max_amount_per_payment": "$0.02"})
register_exact_evm_client(client, EthAccountSigner(Account.from_key(os.environ["EVM_PRIVATE_KEY"])))

with x402_requests(client) as session:
    res = session.get("https://math-geometry.x402tookit.com/cubic-solve?a=1&b=-6&c=11&d=-6")
    print(res.status_code, res.text)