KEVOS® MAKEOS · Mathematics
Quadratic and Cubic Equation Solver
What are the roots of this quadratic or cubic equation?
Real and complex roots of a quadratic (ax² + bx + c = 0) or cubic (ax³ + bx² + cx + d = 0) equation, with the discriminant.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Equation | choice | Quadratic or cubic. |
| Coefficient a | Leading coefficient (must not be zero). | |
| Coefficient b | Second coefficient. | |
| Coefficient c | Third coefficient. | |
| Coefficient d (cubic) | Constant term of a cubic (ignored for a quadratic). |
Method and formulas
- Quadratic: x = (−b ± √(b² − 4ac)) ÷ 2a.
- Cubic: reduce to t³ + pt + q = 0; three real roots by the trigonometric method when the discriminant is positive, otherwise Cardano’s formula.
- Each root is checked by substitution.
- Example: x³ − 6x² + 11x − 6 = 0 has roots 3, 2, 1.
Limitations
- Floating-point arithmetic; repeated roots may show tiny imaginary parts or differences.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Solve design equations that reduce to a quadratic or cubic
- Find dimensions from area or volume relations
- Check hand algebra
Who it is for
- Engineers
- Technicians
- Engineering students
What you get
- All roots (real and complex)
- Discriminant
- Number of real roots
Interpreting the result
- Pick the physically meaningful root (for example positive and within range).
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 32–34. Topic reference; no source tables or recommended settings are reproduced.
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