HP 15c - Manual (Page 187)

Section 13: Finding the Roots of an Equation 187
Because the absolute-value function is minimum near an argument of zero,
specify the initial estimates in that region, for instance 1 and -1. Then
attempt to find a root.
Keystrokes Display
| ¥
Run mode.
1
v 1.0000
Initial estimates.
1
“ –1
´ _ 1 Error 8
This display indicates that no
root was found.
− 0.0000
Clear error display.
As you can see, the HP-15C stopped seeking a root of f(x) = 0 when it
decided that none existed – at least not in the general range of x to which it
was initially directed. The
Error 8 display does not indicate that an ―illegal‖
operation has been attempted; it merely states that no root was found where
_ presumed one might exist (based on your initial estimates).
If the HP-15C stops seeking a root and displays an error message, one of
these three types of conditions has occurred:

If repeated iterations all produce a constant nonzero value for the
specified function, execution stops with the display
Error 8 .

If numerous samples indicate that the magnitude of the function
appears to have a nonzero minimum value in the area being
searched, execution stops with the display
Error 8 .

If an improper argument is used in a mathematical operation as part
of your subroutine, execution stops with the display
Error 0 .
In the case of a constant function value, the routine can see no indication of
a tendency for the value to move toward zero. This can occur for a function
whose first 10 significant digits are constant (such as when its graph levels
off at a nonzero horizontal asymptote) or for a function with a relatively
broad, local ―flat‖ region in comparison to the range of x-values being tried.
In the case where the function's magnitude reaches a nonzero minimum, the
routine has logically pursued a sequence of samples for which the
magnitude has been getting smaller. However, it has not found a value of
x at which the function's graph touches or crosses the x-axis.