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Find Roots of a Quadratic Equation in Java

beginner· Numbers · Math

Problem

The discriminant d = b² − 4ac decides the nature of a quadratic's roots: two real roots when d > 0, one repeated root when d = 0, and a pair of complex roots when d < 0.

Given the coefficients a, b and c of a quadratic equation, find its roots for each of the three discriminant cases.

Input

a=2, b=-7, c=3

Output

3.0 and 0.5

Java Program

Java

public class QuadraticRoots {
    public static void main(String[] args) {
        solve(2, -7, 3);
        solve(1, -6, 9);
        solve(1, 2, 5);
    }

    static void solve(int a, int b, int c) {
        double d = (double) b * b - 4.0 * a * c; // the discriminant decides which case we're in
        System.out.print("a=" + a + ", b=" + b + ", c=" + c + " -> ");

        if (d > 0) {
            double r1 = (-b + Math.sqrt(d)) / (2.0 * a);
            double r2 = (-b - Math.sqrt(d)) / (2.0 * a);
            System.out.println("two real roots: " + r1 + " and " + r2);
        } else if (d == 0) {
            System.out.println("one repeated root: " + (-b / (2.0 * a)));
        } else {
            double real = -b / (2.0 * a);
            double imag = Math.sqrt(-d) / (2.0 * a);
            System.out.println("complex roots: " + real + " + " + imag + "i and " + real + " - " + imag + "i");
        }
    }
}

▶ Run Code

Output

a=2, b=-7, c=3 -> two real roots: 3.0 and 0.5
a=1, b=-6, c=9 -> one repeated root: 3.0
a=1, b=2, c=5 -> complex roots: -1.0 + 2.0i and -1.0 - 2.0i

Core Logic

Computing the discriminant first splits the problem into three cases, and each case applies its own form of the quadratic formula.

How It Works

1d = b² − 4ac is computed as a double, so large coefficients don't overflow int.
2When d > 0, the two roots are (−b ± √d) / 2a.
3When d == 0, both roots collapse to −b / 2a.
4When d < 0, the roots are complex: the real part is −b / 2a and the imaginary part is √(−d) / 2a.