Quadratics

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

equations.quadratic · v1 · renderer math

1. -x^2 + 9x = 0 → x = 0 or x = 9 2. 3x^2 + 3x = 0 → x = -1 or x = 0 3. x^2 + 16x + 63 = 0 → x = -9 or x = -7 4. -3x^2 - 27x = 0 → x = -9 or x = 0 5. -2x^2 - 6x + 36 = 0 → x = -6 or x = 3 6. -x^2 - 14x - 48 = 0 → x = -8 or x = -6

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 Operating System CSPRNG.

seed token 3MYHJBH34TC3DVM43V1PGDW9FG

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.

entropy in

16 bytes

stream used

26 bytes

rejections

duration

578 µs

problems

Seed receipt

Class A · Cryptographic degraded

Drawn from the kernel entropy pool on the server that rendered this page. (The source you picked was unreachable, so we fell back to the kernel.)

source: Operating System CSPRNG
observed: 2026-10-28T22:15:29+00:00
latency: 1508ms
mixed with: nothing — this source stands alone

This source publishes no per-draw proof URL.

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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.

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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