More detailed NOTE for any_root()

Author: GiacomoPope

src/sage/rings/polynomial/polynomial_element.pyx

@@ -2478,11 +2478,11 @@ cdef class Polynomial(CommutativePolynomial):
             For finite fields, ``any_root()`` is non-deterministic when
             finding linear roots of a polynomial over the base ring.
             However, if ``degree`` is greater than one, or ``ring`` is an
-            extension of the base ring, then eventually the root is found
-            by returning a single root after factorisation. Roots found
+            extension of the base ring, then the root computed is found
+            by attempting to return a root after factorisation. Roots found
             in this way are deterministic. This may change in the future.
             For all other rings or fields, roots are found by first
-            fully-factoring the polynomial and the output is deterministic.
+            fully-factoring ``self`` and the output is deterministic.
 
         EXAMPLES::