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f(x)
ia
f(x)
A
1ic
f(x)
1id
Figure B-1. Functions for Which a Root Can be Found
In most situations, the calculated root is an accurate estimate of the
theoretical, infinitely precise root of the equation. An "ideal" solution
is one for which f(x)=0. However, a non-zero value for f(x) is often
also acceptable because it results from approximating numbers with
limited (12-digit) precision.
Interpreting Results
will display an answer:
B If it finds an estimate for which f(x) equals 0 (see figure B-2a).
® If it finds an estimate where f(x) is not equal to 0, but the calculated
root is a 12-digit number adjacent to the place where the function's
graph crosses the x-axis (see figure B-2b). This occurs when the two
final estimates are neighbors (that is, they differ by 1 in the 12th
digit), and the function's value is positive for one estimate and neg-
ative for the other. In most cases, f(x) will be relatively close to 0.
158
B: More About Solving Equations
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