Solution
= Solution
The <Newton root-finding iteration> is
$$
\boxed{x_{k+1}=x_k-\frac{x_k^6-5x_k^4+6}{6x_k^5-20x_k^3}.}
$$
It is defined when $x_k\notin\{0,\pm\sqrt{10/3}\}$. Finding an exact <zero of a function> is a stopping condition, rather than a reason to continue dividing.