Add QuadraticEquationSolver and test cases (#5619)

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[] {};
+    }
+}