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SOLVING POLYNOMIALS BY SUCCESSIVE SYNTHETIC DIVISION
TI-82 & TI-83/Plus

This is a 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 a solution if the roots are either imaginary or real. Nevertheless, it is left to the student to choose the method from the menu. A quadratic with either real or imaginary roots may be solved by selecting item 6 from the menu after first entering the quadratic coefficients.

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, L1, 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 413 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, you can find it in Chapter 16 of the TI-83 User's Guide. 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  .

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:  Version V1.0, date 8/28/03.  Version V1.1, date 10/2/04

SLVPOLY2

   

Disp "V1.1"

   

Disp "FKizer"

   

Lbl 0

   

Lbl 5

   

Input  "COEFFS=",L1

   

2→I

   

dim(L1)→N

   

{0}→L2

   

N→dim(L2)

   

Lbl 7

   

Menu ("SELECT","FIRST ZERO",1, "RETRY",2, "NEXT ZERO",3,"SLV RED QDRTC",4,"STRT OVR",5,"SLV NEW QDRTC",6 )

   

Lbl 1

   
Input "ZERO=", Z    
L1(1)→L2(1)    
For (I,2,N)    

Z*L2(I-1)+L1(I)→L2(I)

   

End

   

Disp "NEW EQUA",L2

   

Disp "REM=", L2(N)

   

Pause

   

Goto 7

   

Lbl 2

   

Goto 1

   

Lbl 3

   

N-1® N

   

N® dim(L1)

   

N® dim(L2)

   

L2® L1

   

Goto 1

   

Lbl 4

   

L2(1) ® A

   

L2(2) ® B

   

L2(3) ® C

   

a +bi

   

Disp "X1 IS ",(-B+Ö (B2-4AC))/(2A)

   

Disp "AND X2 IS ",(-B-Ö (B2-4AC))/(2A)

   

Stop

   
Lbl 6    
L1L2    
Goto 4    

 Revised 10/1/04