Chapter 3.4, Problem 7E

(General math) a. Write, compile, and run a C++ program to compute and display the value of the second-order polynomial $a{x}^2+bx+c$ for any user-entered values of the coefficients a, b, c, and the variable x. Have your program display a message to inform users what the program does, and then display suitable prompts to alert users to enter the data. (Hint: Use a prompt such as Enter the coefficient of the x-squared term:.)

b. Check the result of your program written for Exercise 7a by using the following test data:

$\begin{array}{l}Testdataset1:a=0,b=0,c=22,x=56\hfill \\ Testdataset2:a=0,b=22,c=0,x=2\hfill \\ Testdataset3:a=22,b=0,c=0,x=2\hfill \\ Testdataset4:a=2,b=4,c=5,x=2\hfill \end{array}$

After finishing your verification, use your program to complete the following chart

Program Plan Intro

Program plan:

1. The variable a, b and c of type float is used to accept the coefficient of second order polynomial.
2. The variable x of type float is used to accept the value of x of second order polynomial.
3. The variable p of type float calculates the value of second order polynomial.

Program description:

The main purpose of the program is to accept the coefficient of x and value of x and then calculate and display the value of second order polynomial.

Explanation of Solution

Program

#include <iostream>
#include <math.h>
using namespace std;

int main()
{
    // declaration of variables
    float a, b, c;
    float x;
    float p;
    // Input values 
    cout<<"Input values to calculate value of the second-order polynomial :: 
	    ax^2 + bx +c";
    cout<<"\nEnter the coefficient of the x-squared term(a) :: ";
    cin>>a;
    cout<<"\nEnter the coefficient of the x term (b) :: ";
    cin>>b;
    cout<<"\nEnter the coefficient of the term (c) :: ";
    cin>>c;
    cout<<"\nEnter the value of x :: ";
    cin>>x;
    // Calculate value of the second-order polynomial
    p = a * x * x + b * x + c ;
    cout<<"\nThe value of the second-order polynomial  is :: "<<p;
    return 0;
}

Explanation:

In the above program a, b and c accepts the coefficient of x for second order polynomial. The variable x accepts the value of x and then second order polynomial is calculated and displayed.

Sample Output:

Enterthecoefficientofthex-squaredterm(a)::0

Enterthecoefficientofthexterm(b)::0

Enterthecoefficientoftheterm(c)::22

Enterthevalueofx::56

Thevalueofthesecond-orderpolynomialis::22

Program Plan Intro

To check the given program for the test values as follows:

Test data set 1: a = 0, b = 0, c = 22, x = 56

Test data set 2: a = 0, b = 22, c = 0, x = 2

Test data set 3: a = 22, b = 0, c = 0, x = 2

Test data set 4: a = 2, b = 4, c = 5, x = 2

To complete the following chart:

a	b	c	x	Polynomial Value
2.0	17.0	-12.0	1.3
3.2	2.0	15.0	2.5
3.2	2.0	15.0	-2.5
-2.0	10.0	0.0	2.0
-2.0	10.0	0.0	4.0
-2.0	10.0	0.0	5.0
-2.0	10.0	0.0	6.0
5.0	22.0	18.0	8.3
4.2	-16.0	-20.0	-5.2

Explanation of Solution

Given Program

#include <iostream>
#include <math.h>
using namespace std;

int main()
{
    // declaration of variables
    float a, b, c;
    float x;
    float p;
    // Input values 
    cout<<"Input values to calculate value of the second-order polynomial :: 
	    ax^2 + bx +c";
    cout<<"\nEnter the coefficient of the x-squared term(a) :: ";
    cin>>a;
    cout<<"\nEnter the coefficient of the x term (b) :: ";
    cin>>b;
    cout<<"\nEnter the coefficient of the term (c) :: ";
    cin>>c;
    cout<<"\nEnter the value of x :: ";
    cin>>x;
    // Calculate value of the second-order polynomial
    p = a * x * x + b * x + c ;
    cout<<"\nThe value of the second-order polynomial  is :: "<<p;
    return 0;
}

Explanation:

Test data set 1:

a = 0, b = 0, c = 22, x = 56

Sample Output:

Input values to calculate value of the second-order polynomial :: ax^2 + bx +c

Enterthecoefficientofthex-squaredterm(a)::0

Enterthecoefficientofthexterm(b)::0

Enterthecoefficientoftheterm(c)::22

Enterthevalueofx::56

Thevalueofthesecond-orderpolynomialis:: 22

Test data set 2:

a = 0, b = 22, c = 0, x = 2

Sample Output:

Input values to calculate value of the second-order polynomial :: ax^2 + bx +c

Enter the coefficient of the x-squared term(a) :: 0

Enter the coefficient of the x term (b) :: 22

Enter the coefficient of the term (c) :: 0

Enter the value of x :: 2

The value of the second-order polynomial is :: 44

Test data set 3:

a = 22, b = 0, c = 0, x = 2

Sample Output:

Input values to calculate value of the second-order polynomial :: ax^2 + bx +c

Enter the coefficient of the x-squared term(a) :: 22

Enter the coefficient of the x term (b) :: 0

Enter the coefficient of the term (c) :: 0

Enter the value of x :: 2

The value of the second-order polynomial is :: 88

Test data set 4:

a = 2, b = 4, c = 5, x = 2

Sample Output

Input values to calculate value of the second-order polynomial :: ax^2 + bx +c

Enter the coefficient of the x-squared term(a) :: 2

Enter the coefficient of the x term (b) :: 4

Enter the coefficient of the term (c) :: 5

Enter the value of x :: 2

The value of the second-order polynomial is :: 21

Chart

Following chart displays the polynomial value for different values of a, b, c and x.

a	b	c	x	Polynomial Value
2.0	17.0	-12.0	1.3	13.480
3.2	2.0	15.0	2.5	40.000
3.2	2.0	15.0	-2.5	30.000
-2.0	10.0	0.0	2.0	12.000
-2.0	10.0	0.0	4.0	8.000
-2.0	10.0	0.0	5.0	0.000
-2.0	10.0	0.0	6.0	-12.000
5.0	22.0	18.0	8.3	545.050
4.2	-16.0	-20.0	-5.2	176.768