What this calculator does
Solve a cubic polynomial ax³ + bx² + cx + d = 0 for all real or complex roots.
How it works
The calculator evaluates roots solve ax³ + bx² + cx + d = 0 using the depressed-cubic (Cardano) form. Inputs are checked before calculation, and invalid values such as zero denominators or out-of-range selections produce a clear error instead of a misleading result.
Input query strings and outputs
Use an input name in this page’s URL as ?name=value, and join additional inputs with &. Portable shared links may instead use the compact ?ac= state parameter.
Input query strings
4-
?a=Coefficient aNumber · Required · Default: 1
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?b=Coefficient bNumber · Required · Default: -6
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?c=Coefficient cNumber · Required · Default: 11
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?d=Coefficient dNumber · Required · Default: -6
Outputs
3-
rootsRootsText · Primary output
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discriminantCubic discriminantNumber
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classificationRoot classificationText
Inputs and results
The inputs are Coefficient a, Coefficient b, Coefficient c, Coefficient d. Results include Roots, Cubic discriminant, Root classification.