Polynomial equation

A polynomial equation has the form $p(x_1,\dots ,x_n)=0$ for a polynomial $p$. Its solutions are the points at which that polynomial vanishes.

A cubic equation is a polynomial equation of degree of a polynomial three, $a{x}^3+b{x}^2+cx+d=0$, with $a\ne 0$. Its three complex roots of a polynomial, counted with multiplicity of a root, need not all have physical significance in an application; a model often selects a branch by continuity from a known limit.