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C++ : Find All Roots of a Quadratic Equation

Tutorial by:Manisha Dubey      Date: 2016-06-18 04:14:48

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For a quadratic equation ax2+bx+c = 0 (where a, b and c are coefficients), it's roots is given by following the formula.

Formula to find root of an quadratic equation


 

This program below asks user to enter coefficients a, b and c and computes the roots of a quadratic equation.

#include <iostream>
#include <cmath>
using namespace std;

int main() {

    float a, b, c, x1, x2, determinant, realPart, imaginaryPart;
    cout << "Enter coefficients a, b and c: ";
    cin >> a >> b >> c;
    determinant = b*b - 4*a*c;
    
    if (determinant > 0) {
        x1 = (-b + sqrt(determinant)) / (2*a);
        x2 = (-b - sqrt(determinant)) / (2*a);
        cout << "Roots are real and different." << endl;
        cout << "x1 = " << x1 << endl;
        cout << "x2 = " << x2 << endl;
    }
    
    else if (determinant == 0) {
        cout << "Roots are real and same." << endl;
        x1 = (-b + sqrt(determinant)) / (2*a);
        cout << "x1 = x2 =" << x1 << endl;
    }

    else {
        realPart = -b/(2*a);
        imaginaryPart =sqrt(-determinant)/(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

We have used sqrt() function to find square root which is a standard library function.

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