C++ Program To Find The Roots Of Quadratic Equation

Given a quadratic equation in the form ax² + bx + c, find roots of it. 

Examples:

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  

Below is the direct formula for finding the roots of the quadratic equation.

There are the following important cases:

1. If b*b < 4*a*c, then roots are complex (not real).
Example: 
roots of x² + x + 1, roots are: 
-0.5 + i0.86603 and -0.5 – i0.86603

2. If b*b == 4*a*c, then roots are real and both roots are same.
Example: 
roots of x² – 2x + 1 are 1 and 1

3. If b*b > 4*a*c, then roots are real and different.
Example:
roots of x² – 7x – 12 are 3 and 4

Roots of Quadratic Equation Flowchart 

Below is the C++ program to implement the above approach:

C++

// C++ program to find roots of
// a quadratic equation
#include <bits/stdc++.h>
using namespace std;

// Prints roots of quadratic equation
// ax*2 + bx + x
void findRoots(int a, int b, int c)
{
    // If a is 0, then equation is
    // not quadratic, but linear
    if (a == 0) {
        cout << "Invalid";
        return;
    }

    int d = b * b - 4 * a * c;
    double sqrt_val = sqrt(abs(d));

    if (d > 0) {
        cout << "Roots are real and different ";
        cout << (double)(-b + sqrt_val) / (2 * a) << " "
             << (double)(-b - sqrt_val) / (2 * a);
    }
    else if (d == 0) {
        cout << "Roots are real and same ";
        cout << -(double)b / (2 * a);
    }

    // d < 0
    else {
        cout << "Roots are complex ";
        cout << -(double)b / (2 * a) << " + i"
             << sqrt_val / (2 * a) << " "
             << -(double)b / (2 * a) << " - i"
             << sqrt_val / (2 * a);
    }
}

// Driver code
int main()
{
    int a = 1, b = -7, c = 12;

    // Function call
    findRoots(a, b, c);
    return 0;
}

Output

Roots are real and different 4 3

The complexity of the above method

Time Complexity: O(log(D)), where D is the discriminant of the given quadratic equation.

Auxiliary Space: O(1)