HP 32SII - Manual (Page 317)

More about Solving C–3
File name 32sii-Manual-E-0424
Printed Date : 2003/4/24 Size : 17.7 x 25.2 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 9 see the previous
estimate of the root (x), which was left in the Y–register. Press 9 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:
–2x 3 + 4x 2 – 6x + 8 = 0
Enter the equation as an expression: