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But this will not apply if a is zero, so that condition must be checked separately. The formula also fails to work (for real numbers) if the expression under the square root is negative. That expression b2 - 4ac is called the discriminant of the quadratic. We define that as the separate variable d and check its sign: #include <iostream.h> #include cmath.h> // needed for the sqrt() function // This solves the equation a*x*x + b*x + c == 0: main0 float a, b, c; tout cc "Enter coefficients of quadratic equation: '; tin >> a >> b >> c; if (a == 0) { tout << "This is not a quadratic equation: a == O\n"; return 0; ) tout cc "The equation is: ' CC a CC "~~2 + ' -CC b << " x + " cc c << ' = O\n"; double d, xl, x2; d = b*b - 4*a*c*I // the discriminant if (d c 0) { tout << 'This equation has no real solutions: d < O\n"; return 0; xl = (-b + sqrt(d))/(2*a); x2 = (-b - sqrt Cd) > / U*a> ; tout << "The solutions are: ' -CC xl << ', ' C-C x2 << endl;
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Note how we use the return statement inside the conditionals to terminate the program if either a is zero or d is negative. The alternative would have be to use e 1 se clauses after each i f.
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CONDITIONAL STATEMENTS AND INTEGER TYPES
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2.21 2.22 Write a single assignment statement that uses the conditional expression operator to assign the absolute value of x to absx. Construct a logical expression to represent each of the following conditions: a. weight is greater than or equal to 115 but less than 125. b. ch is either I Q i or 1q I . c. x is even but not 26. d. donation is in the range 1000-2000 or guest is 1. e. ch is a lowercase or an uppercase letter.
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Construct a truth table for each of the following boolean expressions, showing its truth
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value (0 or 1) for all 4 combinations of truth values of its operands p and q.
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a. !p II q
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b. p scsc q
!p &SC !q c. (p II q) &SC ! (p SC& q)
Use truth tables to determine whether the two boolean expressions in each of the following are equivalent. s a. ! (p scsc q),and !p SCGC !q b . !!p,and p c . !p II q,andp II !g d. p 6~6~ (q SC& r), and (p scsc q) scsc r e. p II (q SC& r), and (p II q) &SC r Write a single C++ statement that prints too many if the variable count exceeds 100, using a. an if statement; b. the conditional expression operator.
Supplementary Programming Problems
2.26 Rewrite the Hello World program so that it reads the user s three initials as input and prints them instead of World! For example, if the user enters R, W, and D, the output would be
Hello, R. W. D.
2.27 2.28
Write and run a program that reads four integers and prints them in the opposite order. Write and run a program that reads four integers and prints the minimum and maximum. Use the conditional statements as in Example 2.8. Write and run a program that reads a grade, A, B, C, D, or F and then prints excellent, good, fair, poor, or failure. Use the e 1 se i f structure. Write and run a program that prints the truth tables for each of the boolean expressions in Problem 2.23. Write and run a program that prints the truth tables to verify your answers to Problem 2.24.
CHAP. 21
CONDITIONAL STATEMENTS AND INTEGER TYPES
The 1993 U.S. Tax Rate Schedule for taxpayers with single status reads:
Table 2.1 Schedule X If the amount on Form 1040, line 37, is: OverBut not over$22,100 53,500 115,000 250,000 -------
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