Quartic equations. Methods for solving fourth degree equations

An algebraic equation of the fourth degree is an equation of the form a(x)=0, where a(x)=a₀x⁴ + a₁x³ + a₂x² + a₃x + a₄,
the coefficients a_i are real (or complex) numbers, and a₀ ≠ 0.
According to the fundamental theorem of algebra, quartic equation always has 4 roots (taking into account multiplicity). As is known, for equations with real coefficients, if the root of the equation is a complex number, then the complex conjugate will also be its root. Thus, for a fourth-degree equation with real coefficients, the following combinations of four roots are possible:
1) four real roots (distinct or multiple);
2) two pairs of complex conjugate roots;
3) two real (distinct or multiple) and two complex conjugate roots.

Methods for solving equations of the fourth degree

Solving equations of the fourth degree by factorization

Solving of symmetric equations of the fourth degree

Ferrari's method for solving fourth degree equations