# C++ Program to Find All Roots of a Quadratic Equation.

In this example, we will learn program that accepts coefficients of a quadratic equation from the user and displays the roots (both real and complex roots depending upon the discriminant).

To understand this example, you should have the knowledge of the following C++ programming topics:

## Program to Find All Roots of a Quadratic Equation

For a quadratic equation **ax ^{2}+bx+c = 0** (where a, b and c are
coefficients), it's roots is given by following the formula.

**Example**

Input : a = 1, b = -2, c = 1 Output : Roots are real and same 1 Input : a = 1, b = 7, c = 12 Output : Roots are real and different -3, -4 Input : a = 1, b = 1, c = 1 Output : Roots are complex -0.5 + i1.73205 -0.5 - i1.73205

The term `b`

is known as the discriminant of a
quadratic equation. The discriminant tells the nature of the roots.^{2}-4ac

- If discriminant is greater than 0, the roots are real and different.
- If discriminant is equal to 0, the roots are real and equal.
- If discriminant is less than 0, the roots are complex and different.

Example:

Ifb, then roots are complex (not real). For example roots of x^{2}< 4*a*c^{2}+ x + 1, roots are -0.5 + i1.73205 and -0.5 - i1.73205 Ifb, then roots are real and both roots are same. For example, roots of x^{2}== 4*a*c^{2}- 2x + 1 are 1 and 1 Ifb, then roots are real and different. For example, roots of x^{2}> 4*a*c^{2}- 7x - 12 are 3 and 4

## Example 1: Program to Find Roots of a Quadratic Equation.

```
#include <iostream>
#include <cmath>
using namespace std;
int main() {
float a, b, c, x1, x2, discriminant, realPart, imaginaryPart;
cout << "Enter coefficients a, b and c: ";
cin >> a >> b >> c;
discriminant = b*b - 4*a*c;
if (discriminant > 0) {
x1 = (-b + sqrt(discriminant)) / (2*a);
x2 = (-b - sqrt(discriminant)) / (2*a);
cout << "Roots are real and different." << endl;
cout << "x1 = " << x1 << endl;
cout << "x2 = " << x2 << endl;
}
else if (discriminant == 0) {
cout << "Roots are real and same." << endl;
x1 = -b/(2*a);
cout << "x1 = x2 =" << x1 << endl;
}
else {
realPart = -b/(2*a);
imaginaryPart =sqrt(-discriminant)/(2*a);
cout << "Roots are complex and different." << endl;
cout << "x1 = " << realPart << "+" << imaginaryPart << "i" << endl;
cout << "x2 = " << realPart << "-" << imaginaryPart << "i" << endl;
}
return 0;
}
```

**Output **

Enter coefficients a, b and c: 4 5 1 Roots are real and different. x1 = -0.25 x2 = -1

In this program, `sqrt()`

library function is used to find the square root of a number.

## Example 2: Program to Find Roots of a Quadratic Equation.

```
#include <iostream>
#include <cmath>
using namespace std;
int main() {
float a, b, c, d, root1, root2;
cout << "Enter coefficients a, b and c: ";
cin >> a >> b >> c;
d = b*b - 4*a*c;
if (d == 0) {
root1 = (-b + sqrt(d)) / (2*a);
root2=root1;
cout << "Roots are real and equal." << endl;
}
else if (d > 0) {
root1 = (-b + sqrt(d)) / (2*a);
root2 = (-b - sqrt(d)) / (2*a);
cout << "Roots are real and different." << endl;
}
else {
root1 = -b/(2*a);
root2 =sqrt(-d)/(2*a);
cout << "Roots are complex and different." << endl;
}
cout << "\nroot1 = " << root1 << "\nroot2 =" << root2;
return 0;
}
```

**Output **

Enter coefficients a, b and c: 1.0 10.0 1.5 Roots are real and different. root1 = -0.0502524 root2 =-9.94975

In these program, `cmath`

preprocessor and `sqrt()`

library function is used to find the square root of a number.

## Next Example

We hope that this Example helped you develop better understanding of the concept of "Find the Roots of a Quadratic Equation" in C++.

**Keep Learning : )**

In the next Example, we will learn about C++ `Find Sum of Natural Numbers`

.