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.
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