HP 50g HP 50g_user's manual_English_HDPSG49AEM8.pdf - Page 84

FCOEF([2,1,0,3,-5,2,1,-2,-3,-5])='(X--5)^2*X^3*(X-2)/(X-+3)^5*(X-1)^2' If you press µ„î` (or, simply µ, in RPN mode) you will get: '(X^6+8*X^5+5*X^4-50*X^3)/(X^7+13*X^6+61*X^5+105*X^445*X^3-297*X62-81*X+243)' 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. 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. - ((1-i*√3)/2) -1. 3 1. 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 5-11