The FROOTS function

The function FROOTS obtains the roots and poles of a fraction. As an example, applying function FROOTS to the result produced above, will result in: [1 –2 –3 –5 0 3 2 1 –5 2]. The result shows poles followed by their multiplicity as a negative number, and roots followed by their multiplicity as a positive number. In this case, the poles are (1, -3) with multiplicities (2,5) respectively, and the roots are (0, 2, -5) with multiplicities (3, 1, 2), respectively.

Another example is: FROOT(‘(X^2-5*X+6)/(X^5-X^2)’) = [0,–2,1, –1,3,1,2, 1], i.e., poles = 0 (2), 1(1), and roots = 3(1), 2(1). If you have had Complex mode selected, then the results would be: [0 –2 1 –1 ‘-((1+i*√3)/2’ –1].

Step-by-step operations with polynomials and fractions

By setting the CAS modes to Step/step the calculator will show simplifications of fractions or operations with polynomials in a step-by-step fashion. This is very useful to see the steps of a synthetic division. The example of dividing

X 3 − 5X 2 + 3X − 2

X− 2

is shown in detail in Appendix C of the calculator’s User’s Guide. The following example shows a lengthier synthetic division:

X 9 − 1

X 2 − 1

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