Quadratics

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

equations.quadratic · v1 · renderer math

1. 3x^2 - 12x = 0 → x = 0 or x = 4 2. -x^2 + 11x - 28 = 0 → x = 4 or x = 7 3. 3x^2 + 3x - 6 = 0 → x = -2 or x = 1 4. 4x^2 + 20x + 24 = 0 → x = -3 or x = -2 5. -2x^2 + 22x - 36 = 0 → x = 2 or x = 9 6. 4x^2 - 16x - 128 = 0 → x = -4 or x = 8

entropy in

16 bytes

stream used

34 bytes

rejections

duration

1,127 µs

problems

Seed receipt

Class C · Observational

The ISS was over 33.42° N, 94.78° E — 2,050 km west of Beijing — when this was drawn.

Carries only tens of bits of genuine surprise. Always mixed with the OS CSPRNG.

source: ISS Position
observed: 2026-09-13T18:46:01+00:00
latency: 189ms
mixed with: csprng — always

https://www.openstreetmap.org/#map=3/33.42/94.78 ↗

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The token is the seed, so this link recomputes the result rather than looking it up. No database, and it works for as long as v1 does.

Controls · from schema()

Root type

Leading coefficient 1

Off lets the x² term carry a coefficient.

How many

1 50

Entropy source

Picking a source changes the story on the receipt, never the quality: anything below class A is mixed with the OS CSPRNG before it reaches you. This result actually came from ISS Position.

seed token QTAGC3W25144907D36785MHXJ4

Re-render keeps this token. Generate replaces it. That is the whole idea.

Printable worksheet 20 problems · answers on page 2

The seed is printed in the footer, so the same sheet comes back from the same link — and a different seed is a different sheet.

This page and /api/v1/g/equations.quadratic run the same code. There is no private endpoint.

Quadratics

Result

Measurements

Seed receipt

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