HP 49g manual Step-by-step operations with polynomials and fractions, Froots function, 5X 2 + 3X

The FROOTS function

The function FROOTS, in the ARITHMETIC/POLYNOMIAL menu, 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: FROOTS(‘(X^2-5*X+6)/(X^5-X^2)’) = [0 –2. 1 –1. 3 1.

21.], 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. ‘-((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 (DIV2 is available in the ARITH/POLYNOMIAL menu):

X 9 −1

X 2 −1

Page 5-12