HP 33s hp 33s_user's manual_English_E_HDPM20PIE56.pdf - Page 327
Interpreting Results, Cases Where a Root Is Found
UPC - 082916001456
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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) f (x) x x a 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: -2x3 + 4x2 - 6x + 8 = 0 Enter the equation as an expression: More about Solving D-3