HP 15c - Manual (Page 222)

222 Appendix D: A Detailed Look at _
 The function's graph is either
convex everywhere or concave
everywhere.
 The only local minima and
maxima of the function's graph
occur singly between adjacent
zeros of the function.
In addition, it is assumed that the _ algorithm will not be interrupted
by an improper operation.
Accuracy of the Root
When you use the _ key to find a root of an equation, the root is
found accurately. The displayed root either gives a calculated function value
(f(x)) exactly equal to zero or else is a 10-digit number virtually adjacent to
the place where the function's graph crosses the x-axis. Any such root has
an accuracy within two or three units in the 10th significant digit.
In most situations the calculated root is an accurate estimate of the
theoretical (infinitely precise) root of the equation. However, certain
conditions can cause the finite accuracy of the calculator to give a result that
appears to be inconsistent with your theoretical expectation.