*In This Tutorial the program 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 program, you should have the knowledge of following C++ programming topics:

- C++ if, if…else and Nested if…else

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.

The term `b`

is known as the discriminant of a quadratic equations. 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: 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 + sqrt(discriminant)) / (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.