feat: add QuadraticEquationSolver and test cases

DIRECTORY.md

@@ -377,6 +377,7 @@
             * [PrimeFactorization](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/PrimeFactorization.java)
             * [PronicNumber](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/PronicNumber.java)
             * [PythagoreanTriple](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/PythagoreanTriple.java)
+            * [QuadraticEquationSolver](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/QuadraticEquationSolver.java)
             * [ReverseNumber](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/ReverseNumber.java)
             * [RomanNumeralUtil](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/RomanNumeralUtil.java)
             * [SecondMinMax](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/SecondMinMax.java)

src/main/java/com/thealgorithms/maths/QuadraticEquationSolver.java

@@ -0,0 +1,60 @@
+package com.thealgorithms.maths;
+
+/**
+ * This class represents a complex number which has real and imaginary part
+ */
+class ComplexNumber {
+    Double real;
+    Double imaginary;
+
+    ComplexNumber(double real, double imaginary) {
+        this.real = real;
+        this.imaginary = imaginary;
+    }
+
+    ComplexNumber(double real) {
+        this.real = real;
+        this.imaginary = null;
+    }
+}
+
+/**
+ * Quadratic Equation Formula is used to find
+ * the roots of a quadratic equation of the form ax^2 + bx + c = 0
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/Quadratic_equation">Quadratic Equation</a>
+ */
+public class QuadraticEquationSolver {
+    /**
+     * Function takes in the coefficients of the quadratic equation
+     *
+     * @param a is the coefficient of x^2
+     * @param b is the coefficient of x
+     * @param c is the constant
+     * @return roots of the equation which are ComplexNumber type
+     */
+    public ComplexNumber[] solveEquation(double a, double b, double c) {
+        double discriminant = b * b - 4 * a * c;
+
+        // if discriminant is positive, roots will be different
+        if (discriminant > 0) {
+            return new ComplexNumber[] {new ComplexNumber((-b + Math.sqrt(discriminant)) / (2 * a)), new ComplexNumber((-b - Math.sqrt(discriminant)) / (2 * a))};
+        }
+
+        // if discriminant is zero, roots will be same
+        if (discriminant == 0) {
+            return new ComplexNumber[] {new ComplexNumber((-b) / (2 * a))};
+        }
+
+        // if discriminant is negative, roots will have imaginary parts
+        if (discriminant < 0) {
+            double realPart = -b / (2 * a);
+            double imaginaryPart = Math.sqrt(-discriminant) / (2 * a);
+
+            return new ComplexNumber[] {new ComplexNumber(realPart, imaginaryPart), new ComplexNumber(realPart, -imaginaryPart)};
+        }
+
+        // return no roots
+        return new ComplexNumber[] {};
+    }
+}

src/test/java/com/thealgorithms/maths/QuadraticEquationSolverTest.java

@@ -0,0 +1,50 @@
+package com.thealgorithms.maths;
+
+import org.junit.jupiter.api.Assertions;
+import org.junit.jupiter.api.Test;
+
+public class QuadraticEquationSolverTest {
+    private final QuadraticEquationSolver quadraticEquationSolver = new QuadraticEquationSolver();
+
+    @Test
+    public void testSolveEquationRealRoots() {
+        // 4.2x^2 + 8x + 1.9 = 0
+        double a = 4.2;
+        double b = 8;
+        double c = 1.9;
+
+        ComplexNumber[] roots = quadraticEquationSolver.solveEquation(a, b, c);
+        Assertions.assertEquals(roots.length, 2);
+        Assertions.assertEquals(roots[0].real, -0.27810465435684306);
+        Assertions.assertNull(roots[0].imaginary);
+        Assertions.assertEquals(roots[1].real, -1.6266572504050616);
+        Assertions.assertNull(roots[1].imaginary);
+    }
+
+    @Test
+    public void testSolveEquationEqualRoots() {
+        // x^2 + 2x + 1 = 0
+        double a = 1;
+        double b = 2;
+        double c = 1;
+
+        ComplexNumber[] roots = quadraticEquationSolver.solveEquation(a, b, c);
+        Assertions.assertEquals(roots.length, 1);
+        Assertions.assertEquals(roots[0].real, -1);
+    }
+
+    @Test
+    public void testSolveEquationComplexRoots() {
+        // 2.3x^2 + 4x + 5.6 = 0
+        double a = 2.3;
+        double b = 4;
+        double c = 5.6;
+
+        ComplexNumber[] roots = quadraticEquationSolver.solveEquation(a, b, c);
+        Assertions.assertEquals(roots.length, 2);
+        Assertions.assertEquals(roots[0].real, -0.8695652173913044);
+        Assertions.assertEquals(roots[0].imaginary, 1.2956229935435948);
+        Assertions.assertEquals(roots[1].real, -0.8695652173913044);
+        Assertions.assertEquals(roots[1].imaginary, -1.2956229935435948);
+    }
+}