Double root ($p(x_0)=p^{\prime }(x_0)=0,p^{\prime \prime }(x_0)\ne 0$)

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