Chapter 7.3, Problem 5CE

To determine

To modify the program (3) so that the computer finds and prints the values of the roots when they are real or imaginary. The imaginary roots will be printed in form of $a+bi$ .

Explanation of Solution

Given:

The quadratic equation is of the form $a{x}^2+bx+c$

Calculation:

The following is the required BASIC Program-

10 INPUT “Enter the value of a”: a

20 INPUT “Enter the value of b”: b

30 INPUT “Enter the value of c”: c

40 LET $D=(b\times b-4\times a\times c)$

50 If $D>=0$

60 LET $x_1=(-(b)+sqrt(D))/2\times a$

70 LET $x_2=(-(b)-sqrt(D))/2\times a$

80 ELSE

90 LET $x_1=\left(-(b)+Di\right)/2\times a$

100 LET $x_2=\left(-(b)-Di\right)/2\times a$

110 PRINT “The first root is”: $x_1$

120 PRINT “The second root is”: $x_2$

130 END

DRY RUN of the program:-

INPUT:

Enter the value of a

  $a=1$

Enter the value of b

  $b=1$

Enter the value of c

  $c=2$

OUTPUT:

The first root is $-0.5+1.322i$

The second root is $-0.5-1.322i$