Double root
= Double root
{title2=$p(x_0)=p'(x_0)=0,\quad p''(x_0)\ne0$}
A <root of a polynomial> is double when its <multiplicity of a root> is exactly two. Equivalently, $p(x)=(x-x_0)^2q(x)$ with $q(x_0)\ne0$. A generic small perturbation splits it according to <square-root splitting of a double polynomial root>.