Quadratic Equation Solver & Discriminant
Quadratic Equation Solver & Discriminant: Evaluates discriminant Δ = b² - 4ac = 9 - 8 = 1 > 0 and calculates roots (-b ± √Δ) / 2a.
About this quadratic equation solver & discriminant
Quadratic Equation Solver & Discriminant — browser-based utility.
How this tool works
Calculation and parameter relationship: discriminant=b²−4ac; roots=(−b±√discriminant)/(2a)
- Paste the sample input into “Input”.
- Click “Run locally”.
- Compare “Raw Output Data” with the example; revise inputs when an error is shown.
Worked example
Scenario: Solve a quadratic with two real roots using three coefficients.
Sample input:
Processing: Compute discriminant (-3)²−4×1×2=1 and evaluate the stable q formula to get real parts 2 and 1.
Illustrative output:
Limits and verification
Parameter domains and units: (a,b,c) ∈ ℝ³; a ≠ 0; discriminant < 0 ⇒ roots ∈ ℂ; binary64. Results use binary64 floating-point numbers unless BigInt is stated. Result cards show up to 10 significant digits; raw output retains the serialized value. A null ratio means the model has no meaningful finite value for that ratio; it is not zero.
Examples demonstrate an expected workflow; they do not prove every input or every branch of an external specification. Check important results with an independent source before using them for money, security, compliance, safety, or irreversible file changes.
Browser processing boundary
Tool input is processed by code running in the browser and is not intentionally sent to a CZOA processing API. The page can still request ordinary site assets, analytics, or advertising when those services are enabled. Browser extensions and managed-device software remain outside this tool's control.
Relevant references
These references govern or help explain the format, protocol, or calculation used here. Listing a reference does not claim certification or complete implementation of every optional feature.
- NIST Digital Library of Mathematical Functions, §1.2 — Elementary Algebra
- ECMAScript 2026, §6.1.6.1 Number Type
Content owner: CZOA Tools · Last reviewed: 2026-09-15 · Review methodology
How to use it
- Paste the sample input into “Input”.
- Click “Run locally”.
- Compare “Raw Output Data” with the example; revise inputs when an error is shown.
Frequently asked questions
How does the quadratic solver compute its roots?+
It reads exactly three coefficients a, b, c with nonzero a, computes b²−4ac, then uses a stable q-based quadratic formula. Each root is returned as a re/im object.
What input format does the page accept?+
Enter three whitespace-separated coefficients a b c. The independently verified input is 1 -3 2.
What numerical and result boundaries apply?+
A zero leading coefficient or any count other than three fails. Results use JavaScript Number binary64; negative discriminants produce conjugate complex re/im objects. This is numeric root evaluation, not symbolic factorization proof.
What result does the worked example produce?+
The tool processed 1 -3 2 locally and returned discriminant 1 with roots {re:2,im:0} and {re:1,im:0}.