Chapter 4.6, Problem 3E

To determine

ToRUN the program to display the factorization of the given quadratic trinomial.

Explanation of Solution

Given:

The given quadratic trinomial is $6{\mathrm{x}}^2-55\mathrm{x}+56$

Calculation:

The following is the givenBASICProgram-

10 PRINT “THIS PROGRAM FINDS THE FACTORS OF”
20 PRINT “AX^2+B*X+C”
30 INPUT “ENTER A, B AND C (A, C NONZERO):” A, B, C
40 IF A=0 OR C=0 THEN 30
50 LET FLAG =0
60 FOR M=1 TO SQR (ABS (A))
70 IF INT (A/M) <> A/M OR FLAG <>0 THEN 170
80 LET P=M
90 LET R=A/M
100 FOR N=1 TO ABS (C)
110 IF INT (C/N) <> C/N OR FLAG <> 0 THEN 160
120 LET Q=N
130 LET S=C/N
140 IF P*S+Q*R=B THEN LET FLAG =1
150 IF P*S+Q*R=-B THEN LET FLAG =2
160 NEXT N
170 NEXT M
180 IF FLAG=0 THEN
	PRINT A; “*X^2+”; B; “*X+”; C; “IS IRREDUCIBLE.”
190 IF FLAG=1 THEN
	PRINT “(“; P; “*X+”; Q; “(*(“; R; “*X+”; S ;”)”
200 IF FLAG=2 THEN
	PRINT “(“; P; “*X+”; Q; “(*(“; R; “*X+”; -S ;”)”
210 END

DRY RUN of the program:-

SAMPLE OUTPUT:

THIS PROGRAM FINDS THE FACTORS OF

AX^2+B*X+C ENTER A, B AND C (A, C NONZERO):

  $\mathrm{A}=6,\mathrm{B}=-55,\mathrm{C}=56$

  $(6\mathrm{x}-7)(\mathrm{x}-8)$