HP 49g+ - Manual (Page 90)

Page 5-12
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
2
2 3 5 2 3
−
− + −
X
X X X
is shown in detail in Appendix C of the calculator’s User’s Guide. The
following example shows a lengthier synthetic division:
1
1
2
9
−
−
X
X