HP 33S, User Manual

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More about Solving
D–3
File name 33s-English-Manual-040130-Publication(Edition 2).doc Page : 388
Printed Date : 2004/1/30 Size : 13.7 x 21.2 cm
Interpreting Results
The SOLVE operation will produce a solution under either of the following
conditions:
If it finds an estimate for which f(x) equals zero. (See figure a, below.)
If it finds an estimate where f(x) is not equal to zero, 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, below). 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 negative for the other. Or they are (0,
10
–499
) or (0, –10
–499
). In most cases , f(x) will be relatively close to zero.
f (x)
x
a
f (x)
x
b
Cases Where a Root Is Found
To obtain additional information about the result, press
<
see the previous
estimate of the root ( x ), which was left in the Y–register. Press
<
again to see the
value of f(x) , which was left in the Z–register. If f(x) equals zero or is relatively small,
it is very likely that a solution has been found. However, if f(x) is relatively large,
you must use caution in interpreting the results.
Example: An Equation With One Root.
Find the root of the equation:
–2 x
3
+ 4 x
2
– 6 x + 8 = 0
Enter the equation as an expression: