The Froots Function; Step-By-Step Operations With Polynomials And Fractions - HP 48gII User Manual

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
is shown in detail in Appendix C of the calculator's user's guide. The
following example shows a lengthier synthetic division:
3 − 2 + −
X 5 X 3 X 2
−
X 2
9 −
X 1
2 −
X 1
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