Chapter 4.5, Problem 2E

a.

To determine

Torun the program in exercise 1to find whether the giventrinomial $\mathrm{A}{\mathrm{x}}^2+\mathrm{B}\mathrm{x}\mathrm{y}+\mathrm{C}{\mathrm{y}}^2$ is a perfect square trinomial 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 trinomial is ${\mathrm{x}}^2-56\mathrm{x}\mathrm{y}+784{\mathrm{y}}^2$

Calculation:

The following is the required BASICProgram-

10 INPUT “ENTER A, B AND C:” A, B, C$
20 INPUT “ENTER SIGN OF B;”T$
30LET R=0
40 FOR I=1 TO A
50 IF I*I=A THEN R=I
60 NEXT I
70 LET S=0
80 FOR J=1 TO C
90 IF J*J=C THEN S=I
100 NEXT J
110 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”)”;
120 ELSE PRINT “THE GIVEN TRINOMIAL IS NOT A PERFECT SQUARE TRINOMIAL”

130 END

DRY RUN of the program:-

SAMPLE OUTPUT:

ENTER A, B AND C

  $\mathrm{A}=1,\mathrm{B}=56,\mathrm{C}=784$

THE GIVEN TRINOMIAL IS PERFECT SQUARE TRINOMIAL

AND ITS FACTORISATION ARE $(\mathrm{x}-18)(\mathrm{x}-18)$

b.

To determine

To run the program in exercise 1 to find whether the given trinomial $\mathrm{A}{\mathrm{x}}^2+\mathrm{B}\mathrm{x}\mathrm{y}+\mathrm{C}{\mathrm{y}}^2$ is a perfect square trinomial 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 trinomial is $9{\mathrm{x}}^2+144\mathrm{x}\mathrm{y}+576{\mathrm{y}}^2$

Calculation:

The following is the required BASICProgram-

10 INPUT “ENTER A, B AND C:” A, B, C$
20 INPUT “ENTER SIGN OF B;”T$
30 LET R=0
40 FOR I=1 TO A
50 IF I*I=A THEN R=I
60 NEXT I
70 LET S=0
80 FOR J=1 TO C
90 IF J*J=C THEN S=I
100 NEXT J
110 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”)”;
120 ELSE PRINT “THE GIVEN TRINOMIAL IS NOT A PERFECT SQUARE TRINOMIAL”

130 END

DRY RUN of the program:-

SAMPLE OUTPUT:

ENTER A, B AND C

  $\mathrm{A}=9,\mathrm{B}=144,\mathrm{C}=576$

THE GIVEN TRINOMIAL IS PERFECT SQUARE TRINOMIAL

AND ITS FACTORISATION ARE $(3\mathrm{x}+24)(3\mathrm{x}+24)$

c.

To determine

To run the program in exercise 1 to find whether the given trinomial $\mathrm{A}{\mathrm{x}}^2+\mathrm{B}\mathrm{x}\mathrm{y}+\mathrm{C}{\mathrm{y}}^2$ is a perfect square trinomial 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 trinomial is $64{\mathrm{x}}^2+56\mathrm{x}\mathrm{y}+49{\mathrm{y}}^2$

Calculation:

The following is the required BASICProgram-

10 INPUT “ENTER A, B AND C:” A, B, C$
20 INPUT “ENTER SIGN OF B;”T$
30 LET R=0
40 FOR I=1 TO A
50 IF I*I=A THEN R=I
60 NEXT I
70 LET S=0
80 FOR J=1 TO C
90 IF J*J=C THEN S=I
100 NEXT J
110 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”)”;
120 ELSE PRINT “THE GIVEN TRINOMIAL IS NOT A PERFECT SQUARE TRINOMIAL”

130 END

DRY RUN of the program:-

SAMPLE OUTPUT:

ENTER A, B AND C

  $\mathrm{A}=65,\mathrm{B}=56,\mathrm{C}=49$

THE GIVEN TRINOMIAL IS NOT A PERFECT SQUARE TRINOMIAL

d.

To determine

To run the program in exercise 1 to find whether the given trinomial $\mathrm{A}{\mathrm{x}}^2+\mathrm{B}\mathrm{x}\mathrm{y}+\mathrm{C}{\mathrm{y}}^2$ is a perfect square trinomial 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 trinomial is $625{\mathrm{x}}^2-1050\mathrm{x}\mathrm{y}+441{\mathrm{y}}^2$

Calculation:

The following is the required BASICProgram-

10 INPUT “ENTER A, B AND C:” A, B, C$
20 INPUT “ENTER SIGN OF B;”T$
30 LET R=0
40 FOR I=1 TO A
50 IF I*I=A THEN R=I
60 NEXT I
70 LET S=0
80 FOR J=1 TO C
90 IF J*J=C THEN S=I
100 NEXT J
110 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”)”;
120 ELSE PRINT “THE GIVEN TRINOMIAL IS NOT A PERFECT SQUARE TRINOMIAL”

130 END

DRY RUN of the program:-

SAMPLE OUTPUT:

ENTER A, B AND C

  $\mathrm{A}=625,\mathrm{B}=1050,\mathrm{C}=441$

THE GIVEN TRINOMIAL IS PERFECT SQUARE TRINOMIAL

AND ITS FACTORISATION ARE $(25\mathrm{x}-21)(25\mathrm{x}-21)$