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

Where **a, b** and **c** are coefficient of the equation ax^2 + bx + c = 0 which is in the standard form.

**How to compute?**

The steps to compute quadratic equation is given below.

*Step1:*

The program request 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 ^{2} – 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

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

### Program Code

```
/* 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 <cstdlib>
#include <conio.h>
#include <iostream>
#include <cmath>
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;
t1 = -1 * b;
t2 = term2 (a, b, c);
t3 = sqrt (t2);
root1 = (t1 + t3)/ (2 * a);
root2 = (t1 - t3)/ (2 * a);
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.