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

A quadratic equation is in the form ax2 + bx + c. The roots of the quadratic equation are given by the following formula −

There are three cases −

b2 < 4*a*c - The roots are not real i.e. they are complex

b2 = 4*a*c - The roots are real and both roots are the same.

b2 > 4*a*c - The roots are real and both roots are different

The program to find the roots of a quadratic equation is given as follows.

In this program, you’ll learn to find Find Quadratic Equation Roots and All Roots of a Quadratic Equation.

This program accepts coefficients of a quadratic equation from the user and displays the roots (both real and complex roots depending upon the determinant) or just Find Quadratic Equation Roots.

To understand this example to Find Quadratic Equation Roots, you should have the knowledge of following C++ programming topics:

Source Code: 

#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;
}

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