Cubic Real Roots
Find the real roots of a cubic polynomial using its depressed form.
Your numbers
Real roots
Numerical real roots, rounded to 10 significant digits. Near repeated roots, rescaling coefficients improves reliability.
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Formula
x=y−b/(3a); solve y³+py+q=0 with Cardano/trigonometric formulas.
Find the real roots of a cubic polynomial using its depressed form.
Worked example
- Cubic coefficient a
- 1
- Quadratic coefficient b
- -6
- Linear coefficient c
- 11
- Constant d
- -6
- Real roots
- 1, 2, 3
- Distinct real roots
- 3
Scope and limitations
Numerical real roots, rounded to 10 significant digits. Near repeated roots, rescaling coefficients improves reliability.
Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.
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Formula version: 9399fe18387d · Example checked: