Chapter 4.5, Problem 4E

a.

To determine

ToRUN the program in exercise 3 to find whether the trinomial $\mathrm{A}{\mathrm{x}}^2+\mathrm{B}\mathrm{x}\mathrm{y}+\mathrm{C}{\mathrm{y}}^2$ is a perfect square trinomial or the difference of squares for given integers $\mathrm{A},\mathrm{B}$ and $\mathrm{C}$ .

Explanation of Solution

Given:

If the polynomial is perfect square trinomial, the program should print its factorization.

The given polynomial is $144{\mathrm{x}}^2-48\mathrm{x}\mathrm{y}+4{\mathrm{y}}^2$

Calculation:

The following is the required BASICProgram-

10 INPUT “ENTER A, B AND C:” A, B, C$
20 IF B==0 THEN GOTO 40
30 INPUT “ENTER SIGN OF B;”T$
40 LET R=0
50 FOR I=1 TO A
60 IF I*I=A THEN R=I
70 NEXT I
80 LET S=0
90 FOR J=1 TO C
100 IF J*J=C THEN S=I
110 NEXT J
120 IF B==0 AND R==1 AND S==J THEN PRINT 
	“THE GIVEN TRINOMIAL IS DIFFERENCE OF SQUARES”
	 “AND ITS FACTORISATION IS “(“; R ”x+” S”)(“;R ”x-”S”)”;
130 IF R==I AND S==J AND 2*R*S==B THEN PRINT
	“THE GIVEN TRINOMIAL IS PERFECT SQUARE TRINOMIAL”
	“AND ITS FACTORISATION ARE”; “(“; R ”x” TS”)(“;R ”x” TS”)”;
140 ELSE PRINT “THE GIVEN TRINOMIAL IS NOT A PERFECT SQUARE TRINOMIAL”

150 END

DRY RUN of the program:-

SAMPLE OUTPUT:

ENTER A, B AND C

  $\mathrm{A}=144,\mathrm{B}=48,\mathrm{C}=4$

THE GIVEN TRINOMIAL IS PERFECT SQUARE TRINOMIAL

AND ITS FACTORISATION IS $(12\mathrm{x}+2)(12\mathrm{x}+2)$

b.

To determine

To RUN the program in exercise 3 to find whether the trinomial $\mathrm{A}{\mathrm{x}}^2+\mathrm{B}\mathrm{x}\mathrm{y}+\mathrm{C}{\mathrm{y}}^2$ is a perfect square trinomial or the difference of squares for given integers $\mathrm{A},\mathrm{B}$ and $\mathrm{C}$ .

Explanation of Solution

Given:

If the polynomial is perfect square trinomial, the program should print its factorization.

The given polynomial is $144{\mathrm{x}}^2-4{\mathrm{y}}^2$

Calculation:

The following is the required BASICProgram-

10 INPUT “ENTER A, B AND C:” A, B, C$
20 IF B==0 THEN GOTO 40
30 INPUT “ENTER SIGN OF B;”T$
40 LET R=0
50 FOR I=1 TO A
60 IF I*I=A THEN R=I
70 NEXT I
80 LET S=0
90 FOR J=1 TO C
100 IF J*J=C THEN S=I
110 NEXT J
120 IF B==0 AND R==1 AND S==J THEN PRINT 
	“THE GIVEN TRINOMIAL IS DIFFERENCE OF SQUARES”
	 “AND ITS FACTORISATION IS “(“; R ”x+” S”)(“;R ”x-”S”)”;
130 IF R==I AND S==J AND 2*R*S==B THEN PRINT
	“THE GIVEN TRINOMIAL IS PERFECT SQUARE TRINOMIAL”
	“AND ITS FACTORISATION ARE”; “(“; R ”x” TS”)(“;R ”x” TS”)”;
140 ELSE PRINT “THE GIVEN TRINOMIAL IS NOT A PERFECT SQUARE TRINOMIAL”

150 END

DRY RUN of the program:-

SAMPLE OUTPUT:

ENTER A, B AND C

  $\mathrm{A}=144,\mathrm{B}=0,\mathrm{C}=4$

THE GIVEN TRINOMIAL IS DIFFERENCE OF SQUARES

AND ITS FACTORISATION IS $(12\mathrm{x}+2)(12\mathrm{x}-2)$

c.

To determine

To RUN the program in exercise 3 to find whether the trinomial $\mathrm{A}{\mathrm{x}}^2+\mathrm{B}\mathrm{x}\mathrm{y}+\mathrm{C}{\mathrm{y}}^2$ is a perfect square trinomial or the difference of squares for given integers $\mathrm{A},\mathrm{B}$ and $\mathrm{C}$ .

Explanation of Solution

Given:

If the polynomial is perfect square trinomial, the program should print its factorization.

The given polynomial is

  $144{\mathrm{x}}^2-48\mathrm{x}\mathrm{y}+4{\mathrm{y}}^2$

Calculation:

The following is the required BASICProgram-

10 INPUT “ENTER A, B AND C:” A, B, C$
20 IF B==0 THEN GOTO 40
30 INPUT “ENTER SIGN OF B;”T$
40 LET R=0
50 FOR I=1 TO A
60 IF I*I=A THEN R=I
70 NEXT I
80 LET S=0
90 FOR J=1 TO C
100 IF J*J=C THEN S=I
110 NEXT J
120 IF B==0 AND R==1 AND S==J THEN PRINT 
	“THE GIVEN TRINOMIAL IS DIFFERENCE OF SQUARES”
	 “AND ITS FACTORISATION IS “(“; R ”x+” S”)(“;R ”x-”S”)”;
130 IF R==I AND S==J AND 2*R*S==B THEN PRINT
	“THE GIVEN TRINOMIAL IS PERFECT SQUARE TRINOMIAL”
	“AND ITS FACTORISATION ARE”; “(“; R ”x” TS”)(“;R ”x” TS”)”;
140 ELSE PRINT “THE GIVEN TRINOMIAL IS NOT A PERFECT SQUARE TRINOMIAL”

150 END

DRY RUN of the program:-

SAMPLE OUTPUT:

ENTER A, B AND C

  $\mathrm{A}=144,\mathrm{B}=48,\mathrm{C}=2$

THE GIVEN TRINOMIAL IS DIFFERENCE OF SQUARES

AND ITS FACTORISATION IS $(12\mathrm{x}+2)(12\mathrm{x}+2)$

d.

To determine

To RUN the program in exercise 3 to find whether the trinomial $\mathrm{A}{\mathrm{x}}^2+\mathrm{B}\mathrm{x}\mathrm{y}+\mathrm{C}{\mathrm{y}}^2$ is a perfect square trinomial or the difference of squares for given integers $\mathrm{A},\mathrm{B}$ and $\mathrm{C}$ .

Explanation of Solution

Given:

If the polynomial is perfect square trinomial, the program should print its factorization.

The given polynomial is $144{\mathrm{x}}^2+4{\mathrm{y}}^2$

Calculation:

The following is the required BASICProgram-

10 INPUT “ENTER A, B AND C:” A, B, C$
20 IF B==0 THEN GOTO 40
30 INPUT “ENTER SIGN OF B;”T$
40 LET R=0
50 FOR I=1 TO A
60 IF I*I=A THEN R=I
70 NEXT I
80 LET S=0
90 FOR J=1 TO C
100 IF J*J=C THEN S=I
110 NEXT J
120 IF B==0 AND R==1 AND S==J THEN PRINT 
	“THE GIVEN TRINOMIAL IS DIFFERENCE OF SQUARES”
	 “AND ITS FACTORISATION IS “(“; R ”x+” S”)(“;R ”x-”S”)”;
130 IF R==I AND S==J AND 2*R*S==B THEN PRINT
	“THE GIVEN TRINOMIAL IS PERFECT SQUARE TRINOMIAL”
	“AND ITS FACTORISATION ARE”; “(“; R ”x” TS”)(“;R ”x” TS”)”;
140 ELSE PRINT “THE GIVEN TRINOMIAL IS NOT A PERFECT SQUARE TRINOMIAL”

150 END

DRY RUN of the program:-

SAMPLE OUTPUT:

ENTER A, B AND C

  $\mathrm{A}=144,\mathrm{B}=0,\mathrm{C}=4$

THE GIVEN TRINOMIAL IS NOT A PERFECT SQUARE TRINOMIAL