100 REM SAMPLE PROGRAM TO FIND THE
110 REM ROOTS OF THE FUNCTION
120 REM
130 REM Y=(X-3)(X-1)(X+4)
140 REM
150 REM WHICH WE KNOW ARE X=1,3, AND -4.
160 REM
170 REM TRY THE INTERVALS (0,2), (2,0)
180 REM AND (-5,-3)
190 :
200 DEFFNF(X) = (X-3)*(X-1)*(X+4)
210 PRINT
220 INPUT"LEFT ENDPOINT";A
230 INPUT"RIGHT ENDPOINT";B
240 INPUT"TOLERANCE";TL
250 PRINT
260 GOSUB 380
270 IF ER=1 THEN PRINT "NO ZERO WAS FOUND BETWEEN";A;"AND";B: GOTO 210
280 PRINT "ROOT IS AT:";MID: GOTO 210
290 :
300 REM **************************
310 :
320 REM BISECT SUBROUTINE, USED TO
330 REM FIND THE ZERO OF A FUNCTION
340 REM BETWEEN POINTS A AND B, WITH
350 REM TOLERANCE TL.  IF NO ZERO
360 REM EXISTS, ER=1.
370 REM
380 FL=FNF(A): FR=FNF(B): ER=0
390 IF FL*FR > 0 THEN ER=1: RETURN
400 MID = (A+B)/2
410 IF ABS(A-MID) <= TL THEN RETURN
420 FM = FNF(MID)
430 IF FL*FM <= 0 THEN B = MID: GOTO 400
440 A = MID: FL = FM: GOTO 400