HP 15c - Manual (Page 221)

Appendix D: A Detailed Look at _ 221
As discussed in section 13, page 186, the occurrence of other situations in
the iteration process indicates the apparent absence of a function zero. The
reason is that there is no way to logically predict a new estimate that is
likely to have a function value closer to zero. In such cases,
Error 8 is
displayed.
You should note that the initial estimates you provide are used to begin the
"prediction" process. By permitting more accurate predictions than might
otherwise occur, properly chosen estimates greatly facilitate the
determination of the root you seek.
The _ algorithm will always find a root provided one exists
(within the overflow bounds), if any one of four conditions are met:
 Any two estimates have function
values with opposite signs.
 The function is monotonic, meaning
that f(x) either always decreases or
else always increases as x is
increased.