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Polynomial Roots
To gain access to this window, select the menu item File /
Roots of Polynomials. This window is used to find the real roots of
the polynomial Anxn + An-1xn-1 +
... + A1x + A0
First select the order of the polynomial (in the range 1 to 10) by changing the number in the box in the top left, or by clicking on the arrows next to it. The window will change accordingly.
Then enter the coefficients of the polynomial, the highest order coefficient first. The image shows the calculation of the roots of the polynomial
10-15x3 + 3x2 - 4x +
1
When all coefficients are entered, click on the 'Calc' button (or press Enter). The roots found will be displayed, listed in ascending order of value. You can write some notes about the polynomial (click on 'Notes') and write the calculation and results to the log file (click on 'Log') or copy these to the Windows clipboard (click on 'Copy').
You can also save the calculation as a data file to be loaded in at a later
date.
Not an Easy Task
The calculation of the roots of polynomials is often not easy. Some roots can be difficult to find, especially when they are very close together. Small changes to the coefficients can have drastic effects not only on the calculated values of the roots, but also on the number of roots found. Internal rounding errors can also play a significant role. However, with UltimaCalc's ability to work to 128 bit precision (about 38 digits), rounding errors are not normally an issue in practical cases.