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