C++ Program to Solve Quadratic Equations

The C++ program to solve quadratic equations in standard form is a simple program based on the quadratic formula. Given the coefficients as input, it will solve the equation and output the roots of the equation.

This is a simple program is intended for intermediate level C++ programmers.

The program is compiled using Dev-C++ 4.9.9.2 version installed on a Windows 7 64-bit PC. You may try other standard C compilers and the program will still work if you use the correct C libraries.

Problem Definition

In this program, we solve the quadratic equation using the formula.

\begin{aligned}
&x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\
&When\\\\
&ax^2 + bx + c = 0
\end{aligned}

Where a, b and c are coefficient of the equation which is in the standard form.

How to compute quadratic equation?

The steps to compute the quadratic equation is given below.

Step1:

The program requests the input coefficient values a, b and c. When the user input the values, it will compute two terms t1 and t3 and an intermediate term t2.

t1 = -1 * b

Step2:

The function term2 () is called in step 2 and returned value of function is assigned to t2. The term2 () function receives the coefficient values – a, b, c and compute the value for t2.

t2 = term2(a, b, c);

The term () function returns and assign value of b<sup>2</sup> – 4ac to t2 and it is useful in understanding the root of the quadratic equation.

For example,

If (t2 < 0), then the roots are not real

If (t2 == 0) then, there is exactly one root value.

If (t2 > 0) then there are two root values.

The above condition is checked and printed with output values. Now we need to compute the roots and display the output values.

Step3:

A term t3 is assigned value after taking square root of t2.

t3 = sqrt (t2);

Step4:

Finally, we have t1 and t3 to compute two roots of a quadratic equation.

root1 = (t1 + t3)/ 2 * a;
root2 = (t1 + t3)/ 2 * a;

Then root1 and root are calculated and printed immediately.

Flowchart – Program for Quadratic Equations

To understand flow of logic of this program, see the flowchart below.

Program Code – Program for Quadratic Equation

/* C Program to solve a quadratic equation - Ax^2 + Bx + C = 0 using the formula
X1= -b + sqrt (b^2 – 4 * a * c)/ (2 * a) 
and X2 = -b - sqrt (b^2 – 4 * a * c)/ (2* a) */

#include <stdio.h>
#include <stdlib.h>
#include <iostream.h>
#include <cmath.h>

using namespace std;
int main (){

   /* function quadratic */    
   int term2 (int a, int b, int c);

   /* coefficients a, b, c */    
   int a, b, c;    
   float root1, root2, t1, t2, t3;    
   root1 = root2 = 0.0;    
   cout << "\n\n\n\n\n\n";    
   cout << "\t\t\t\tPlease enter coefficients:" << endl;
   cout << "\t\t\t\tA="; cin >> a;    
   cout << "\t\t\t\tB="; cin >> b;    
   cout << "\t\t\t\tC="; cin >> c;    
   cout << "\t\t\t\tA=" << " " << a;    
   cout << "\tB=" << " " << b;    
   cout << "\tC=" << " " << c << endl;    
   cout << endl;    

   //Compute roots
   t1 = -1 * b;    
   t2 = term2 (a, b, c);    
   t3 = sqrt (t2);    
   root1 = (t1 + t3)/ (2 * a);    
   root2 = (t1 - t3)/ (2 * a);    
 
   //Display roots
   cout << "\t\t\t\tRoot-1 =" << " " << root1 << endl;    
   cout << "\t\t\t\tRoot-2 =" << " " << root2 << endl;    
   getch ();    
   return EXIT_SUCCESS;
}


int term2 (int x, int y, int z){    
int p = y * y;    
int q = 4 * x * z;    
int r = p - q;    
if (r < 0)    
   cout << "\t\t\t\tThere is no real root." << endl;    
if (r == 0)    
   cout << "\t\t\t\tThere is only one real root." << endl; 
if (r > 0)    
   cout << "\t\t\t\tThere are two real roots." << endl;    
   return r;
}

Output

The output of the above program is given below.

                    Please enter coefficients:
                    A=1
                    B=22
                    C=44        
                    A= 1      B= 22    C= 44
                    
                    There are two real roots:
                    Root-1 = -2.22504
                    Root-2 = -19.775

C++ Program to Convert Radian to Degree

The program – “C++ Program to Convert Radian to Degree” is based on a simple mathematical concept. The degree is converted to radian value or radian is converted to degrees for computing trigonometric identities.

In this program, we used two formulas for following

• Radian to Degree conversion
• Degree to Radian conversion

This program – C++ Program to Convert Radian to Degree is intended for beginners of C++ programming language and we used Dev C++ 4.9.9.2 compiler to compile and run this program. However, you can use any other standard C++ compiler to compile and execute the program.

To help you learn, go through each section given below,

1. Problem definition
2. Flowchart
3. Program code
4. Output

Problem Definition

In this C++ program, the user makes one of the two choices – perform radian to degree conversion or degree to radian conversion. Since, this program is based simple math, we used formulas given below.

Converting from radian to degree

The formula to convert radians to degree is

Degree = radian * 180/π

Converting from degrees to radians

radian = degree * π/180

When a user start the program, the C++ program does following.

• Ask to choose a conversion method
• Ask input values based on the conversion chosen by the user.
• Use formula for conversion
• Print the output value.

See the flowchart section for logical flow of the program.

Flowchart – Radian to Degree Program

Program Code – Radian to Degree Program

#include <stdio.h>
#include <stdlib.h>
using namespace std;
int main(){    
float radian, degree, pi;    
int choice;    pi = 3.14;
// Menu    
cout << "1.Radian to Degree" << endl;    
cout << "2.Degree to Raidan" << endl;    
cout << "\n\n";    
cout << "Enter Your Choice:”; 
cin >> choice;// Switch starts here
switch (choice){    
   Case 1:    
       cout << "Enter Radian Value to Convert: ";    
       cin << radian;    
       cout << "\n\n";    
       degree = radian * 180/pi;    
       cout << "The Degree Value for" << " " << radian << " " << "radian is" << " "<< degree << " " << "degree" << " " << endl;
       break;   
   Case 2:    
       cout << "Enter Degree Value to Convert:";    
       cin << degree;    cout << "\n\n";    
       radian = degree * pi/180;    
       cout << "The Radian Value for" << " "<< degree << " " << "degree is" << " "<< radian << "radian" << " " << endl;    
       break;    
   default:    
       cout << "Wrong Value! Try again later" << endl;
       }    
system ("pause");    
return EXIT_SUCCESS;
}

Output

The output of the above program is given below. When a user enters the radian measure (0.785) the corresponding degree value is computed and displayed on the console.

1. Radian to Degree
2. Degree to Radian

Enter Your Choice:1
Enter Radian Value for 0.785 radian is 45 degree
Press any key to continue . . .