where a is nonzero; or in other words, a polynomial of degree three. The derivative of a cubic function is a quadratic function. The integral of a cubic function is a quartic function.

Setting ƒ(x) = 0 and assuming a ≠ 0 produces a cubic equation of the form:

Usually, the coefficients a, b,c, d are real numbers. However, most of the theory is also valid if they belong to a field of characteristic other than 2 or 3.

Solving a cubic equation amounts to finding the roots of a cubic function.

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