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SOLVING POLYNOMIALS BY SUCCESSIVE SYNTHETIC DIVISION
Casio CFX-9850/Plus

This is a pseudo menu-driven program that solves polynomials by successively reducing the degree of the polynomial by synthetic division to a quadratic. Although the quadratic could be solved by further synthetic division if it has real zeros, the quadratic solution will provide imaginary roots as well as real roots. Nevertheless, it is left to the student to choose the method from the menu.

To conserve memory, and in deference to those who are going to enter this program by hand, I have written this program so that all coefficients are entered at the same time. As an example, suppose that you want to divide x3+4x2 +6x +3 by x+1. When the program prompts "ZERO=" respond with -1. When it prompts "COEFFS=", respond with {1,4,6,3}. Be sure to use braces rather than brackets or parentheses. Since you’re inputting to a list, List 1, you’ll get an error if you don’t. This is a program using lists. So, if you get errors, first thing to look for is parentheses or brackets where there should be braces.

Memory Usage etc.:  This version of the program uses 421 bytes of memory. I estimate it will take an inexperienced programmer about 20 minutes to enter by hand. If you don't know how to enter the coding, there's a list on page 453 of the Casio Cfx-9850GB Plus User's Guide. Look at page 371 of that same guide for hints on what the coding does. Some of the programs have keystrokes, but I haven't gotten to that on this one yet. I may also include some often-used entries on my web page. Look for it if you need it.

DISCLAIMER:  This program is free, and, therefore, I make no claims about it's efficacy, efficiency, or proper operation.  If you find a problem with this program, or can suggest an improvement, please e-mail me at knosummath@aol.com  .

SNYTAX NOTE: The symbol => is not equal to or greater than, but is the symbol obtained by [SHIFT], [PRGM],[F3],[F3]. The symbol that looks like is not a triangle, but the symbol obtained by [SHIFT], [PRGM],[F3].

Use of this Program:  You may use this program freely for your own personal use and for the use of other students, but use for publication or any means of profit requires my permission.

Revisions:  The first version, V1.0 was posted on 7/29/03.  V1.1 was posted on 9/30/04.  The basic idea is the same, but the first version had a couple typing errors in the coding and one line missing.

Enter the following for the program:

Coding

Keystrokes

Notes

cplyslv1

 

 

"V1.1 FKizer"

 

 

Lbl 0

 

 

Lbl 5

 

 

"COEFFS="?→List 1

 

 

2→I

 

 

Dim List 1® N

 

 

N® Dim List 2

 

 

Lbl 6

 

 

" 1 FIRST ZERO"

 

 

"2 RETRY"

 

 

"3 NEXT ZERO"

 

 

"4 SLV QUADRTC"

 

 

"5 STRT OVER"

 

 

?→S

 

 

S = 1=> Goto 1

 

 

S = 2 =>Goto 2

 

 

S = 3 => Goto 3

 

 

S = 4 =>Goto 4

 

 

S = 5=> Goto 5

 

 

Lbl 1

 

 

"ZERO="?→Z    
For 2®I To N    
List 1[1] List 2[1]    

Z*List 2[I-1]+List 1[I]® List 2[I]

 

Next steps of synthetic Div

Next 

 

 

List 2

 

Displays answer in list 2

Goto 6

 

 

Lbl 2

 

 

"ZERO="?→Z

 

 

2→I

 

 

Goto 1

 

 

Lbl 3

 

 

2→I

 

 

N-1→N

 

To decrease dimension of L2 one l

List 2→List 1

 

Puts answer in list 1

Seq(List1[X, X, 1,DimList 1-1,1→List 1

 

Deletes last entry of list 1

N→Dim List 2

 

Set dim of L2.

Goto 1

 

 

Lbl 4

 

Transfers coeffs to A, B, & C

List 2[1] →A

 

 

List 2[2] →B

 

 

List 2[3] →C

 

 

ClrText

 

 

"X1="

 

Calculates and displays

(-B+Ö (B2-4AC))¸ (2A)

 

 

"X2="

 

 

(-B-Ö (B2-4AC))¸ (2A)

 

Calculates and displays

Stop

 

 

Last Revised: 9/30/04