The Standard Form of a Quadratic Equation looks like this:
ax2 + bx + c = 0
The term b2-4ac is known as the discriminant of a quadratic equation.
The discriminant tells the nature of the roots.
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.
This program accepts coefficients of a quadratic equation from the user and displays the roots (both real and complex roots depending upon the discriminant).
C++ Code:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 | #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:
