The **Standard Form** of a Quadratic Equation looks like this:

ax^{2}+ bx + c = 0

The term ** b** is known as the discriminant of a quadratic equation.

^{2}-4ac

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.

**C# Code:**

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using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Threading.Tasks; namespace ConsoleApp2 { class Program { public static void SolveQuadratic(double a, double b, double c) { double sqrtpart = b * b - 4 * a * c; double x, x1, x2, img; if (sqrtpart > 0) { x1 = (-b + System.Math.Sqrt(sqrtpart)) / (2 * a); x2 = (-b - System.Math.Sqrt(sqrtpart)) / (2 * a); Console.WriteLine("Two Real Solutions: {0,8:f4} or {1,8:f4}", x1, x2); } else if (sqrtpart < 0) { sqrtpart = -sqrtpart; x = -b / (2 * a); img = System.Math.Sqrt(sqrtpart) / (2 * a); Console.WriteLine("Two Imaginary Solutions: {0,8:f4} + {1,8:f4} i or {2,8:f4} + {3,8:f4} i", x, img, x, img); } else { x = (-b + System.Math.Sqrt(sqrtpart)) / (2 * a); Console.WriteLine("One Real Solution: {0,8:f4}", x); } } static void Main(string[] args) { int a, b, c; Console.Write("a : "); a = Int32.Parse(Console.ReadLine()); Console.Write("b : "); b = Int32.Parse(Console.ReadLine()); Console.Write("c : "); c = Int32.Parse(Console.ReadLine()); SolveQuadratic(a, b, c); Console.ReadKey(); } } } |

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