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sci.cubic-equation-Cardano Calculator
Calculates all three roots (real or complex) of a cubic equation ax³+bx²+cx+d = 0 using Cardano's formula and the depressed cubic substitution. The discriminant Δ: Δ > 0 → 3 distinct real roots (casus irreducibilis, requires complex intermediate values); Δ < 0 → one real and two complex conjugate roots.
Inputs
A Coeff
Reference formula or conversion factor shown for context.
B Coeff
Reference formula or conversion factor shown for context.
C Coeff
Reference formula or conversion factor shown for context.
D Coeff
Reference formula or conversion factor shown for context.
Results
depressed cubic p
Reference formula or conversion factor shown for context.
depressed cubic q
Reference formula or conversion factor shown for context.
discriminant Δ
Sample size or count used in the calculation.
real roots
Reference formula or conversion factor shown for context.
x = y - b/3a
Reference formula or conversion factor shown for context.
Newton start (derivative root of x³+px+q)
The instantaneous rate of change — the slope of the tangent line at a point. In physics: derivative of position = velocity; derivative of velocity = acceleration.