Cubic equations. Methods for solving cubic equations

A cubic equation is an algebraic equation of the third degree of the form a(x)=0, where a(x)=a₀x³ + a₁x² + a₂x + a₃,
the coefficients a_i – are real (or complex) numbers, and a₀ ≠ 0.
According to the fundamental theorem of algebra, a cubic equation always has 3 roots (taking into account multiplicity), and at least one of the roots is real, since if the root is a complex number, then its complex conjugate will also be its root. Thus, for a cubic equation the following combinations of three roots are possible:
1) three different real roots;
2) one real root and two complex conjugates;
3) two coinciding real roots (i.e. a root of multiplicity 2) and one that is different from these two real roots;
4) three coinciding real roots (i.e. a root of multiplicity 3).

Methods for solving cubic equations

Solving symmetric cubic equations

Solving cubic equations by factorization

Cardano's formula for solving cubic equations