Chapter 4.5, Problem 1E

To determine

To write a program 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 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.

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

  $\mathrm{A}=4,\mathrm{B}=10,\mathrm{C}=25$

THE GIVEN TRINOMIAL IS PERFECT SQUARE TRINOMIAL

AND ITS FACTORISATION ARE $(2\mathrm{x}+5)(2\mathrm{x}+5)$