Quadratic Equation Solver implementation

Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

Record owner

Guth Instruments

Lifecycle

verified-clean

Evidence ID

t6-004

Effect

Computation or source lookup only

Input and validation requirements

The input a=0 makes the quadratic-formula denominator 2a equal zero. A robust solver must reject it as nonquadratic or explicitly fall back to a linear solver; blindly applying the quadratic formula produces an undefined result.

Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

{
  "inputs": {
    "a": 1,
    "b": -5,
    "c": 6
  },
  "expected_outputs": {
    "roots": [
      "2",
      "3"
    ],
    "vertex": [
      "5/2",
      "-1/4"
    ],
    "axis_of_symmetry": "x = 5/2",
    "discriminant": 1,
    "discriminant_sign": "positive",
    "factoring": "(x - 2)(x - 3)"
  },
  "working": "D = b^2 - 4ac = (-5)^2 - 4(1)(6) = 25 - 24 = 1. sqrt(D) = 1. x = (-b +/- sqrt(D))/(2a) = (5 +/- 1)/2, so x = 6/2 = 3 and x = 4/2 = 2. Vertex x-coordinate h = -b/(2a) = -(-5)/(2(1)) = 5/2. Vertex y-coordinate f(h) = (5/2)^2 - 5(5/2) + 6 = 25/4 - 25/2 + 24/4 = -1/4. Axis: x = 5/2. The polynomial factors as (x - 2)(x - 3)."
}

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche6/tranche6-results.json