How this calculator works
Compute D = b² - 4ac, then evaluate x = (-b ± √D)/(2a). Negative discriminants are represented as complex conjugate roots.
Formula
x = (-b ± √(b² - 4ac)) / (2a)Uses the discriminant to determine and calculate the two roots of ax² + bx + c = 0.
Worked example
x² - 5x + 6 = 0 is a verified test case used by the calculation engine.
Assumptions and limitations
- Coefficient a must be non-zero.
- Inputs are finite real numbers.
Methodology & sources
This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint. Technical calculation version: 1.
- CalcuMint deterministic algebra engine — Standard quadratic formula and vertex identities.
Frequently asked questions
Does it support complex roots?
Yes. A negative discriminant is returned as a pair of complex conjugate roots.
Does it calculate the vertex?
Yes. The deterministic output includes the vertex coordinates.