Find Real & Complex Roots of a Quadratic Equation

Given coefficients a, b, and c of ax^2 + bx + c = 0, find both roots by evaluating the discriminant D = b^2 - 4ac across all three cases: D > 0 (two distinct real roots), D = 0 (equal real roots), and D < 0 (complex conjugate pairs).

Step 1: Start.
Step 2: Read coefficients a, b, c.
Step 3: If a == 0:
         Print 'Not quadratic (Linear equation)' and Stop.
Step 4: Compute Discriminant D = (b * b) - (4 * a * c).
Step 5: If D > 0 (Two distinct real roots):
         root1 = (-b + sqrt(D)) / (2 * a)
         root2 = (-b - sqrt(D)) / (2 * a)
         Print root1, root2.
Step 6: Else if D == 0 (Two equal real roots):
         root1 = -b / (2 * a)
         Print 'Real and Equal Roots:', root1.
Step 7: Else (D < 0, Complex conjugate roots):
         realPart = -b / (2 * a)
         imagPart = sqrt(-D) / (2 * a)
         Print 'Complex Roots: realPart +/- imagPart * i'.
Step 8: Stop.

         +-----------------+
         |     [ START ]   |
         +-----------------+
                  |
                  v
         +-----------------+
         |  Read a, b, c   |
         +-----------------+
                  |
                  v
               /     \
             /  a == 0?\ ---YES--> [Print Not Quadratic] --> [STOP]
             \         /
                  | NO
                  v
         +-----------------+
         | D = b*b - 4*a*c |
         +-----------------+
                  |
                  v
               /     \
             /  D > 0? \ ---YES--> [Distinct Real Roots] --> [STOP]
             \         /
                  | NO
                  v
               /     \
             /  D == 0?\ ---YES--> [Equal Real Roots]   --> [STOP]
             \         /
                  | NO
                  v
         +-----------------------+
         | Complex Roots (with i)| --> [STOP]
         +-----------------------+

Edit the code directly with the Edit Code button, provide custom inputs, and press Run Code to compile and execute in the live terminal console below!

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

int main() {
    double a, b, c;
    cout << "Enter coefficients a, b, and c (ax^2 + bx + c = 0): ";
    if (!(cin >> a >> b >> c)) {
        cout << "Invalid input! Please enter numeric coefficients.\n";
        return 1;
    }

    if (a == 0) {
        cout << "\n[!] Error: Coefficient 'a' cannot be 0 in a quadratic equation.\n";
        if (b != 0) {
            cout << "Linear root (bx + c = 0): x = " << (-c / b) << "\n";
        }
        return 0;
    }

    double D = (b * b) - (4.0 * a * c);
    cout << fixed << setprecision(4);
    cout << "\n========================================\n";
    cout << "Equation      : (" << a << ")x^2 + (" << b << ")x + (" << c << ") = 0\n";
    cout << "Discriminant D: " << D << "\n";
    cout << "----------------------------------------\n";

    if (D > 0) {
        double sqrtD = sqrt(D);
        double root1 = (-b + sqrtD) / (2.0 * a);
        double root2 = (-b - sqrtD) / (2.0 * a);
        cout << "Nature: REAL, UNEQUAL, AND DISTINCT ROOTS\n";
        cout << "Root 1 = " << root1 << "\n";
        cout << "Root 2 = " << root2 << "\n";
    } else if (D == 0) {
        double root = -b / (2.0 * a);
        cout << "Nature: REAL AND EQUAL ROOTS\n";
        cout << "Root 1 = Root 2 = " << root << "\n";
    } else {
        double realPart = -b / (2.0 * a);
        double imagPart = sqrt(-D) / (2.0 * a);
        cout << "Nature: COMPLEX CONJUGATE ROOTS\n";
        cout << "Root 1 = " << realPart << " + " << imagPart << "i\n";
        cout << "Root 2 = " << realPart << " - " << imagPart << "i\n";
    }
    cout << "========================================\n";
    return 0;
}

Input:
1 2 5

Output:
========================================
Equation      : (1.0000)x^2 + (2.0000)x + (5.0000) = 0
Discriminant D: -16.0000
----------------------------------------
Nature: COMPLEX CONJUGATE ROOTS
Root 1 = -1.0000 + 2.0000i
Root 2 = -1.0000 - 2.0000i
========================================