C# Examples

C# Program - Find Roots of a Quadratic Equation

A standard form of a quadratic equation is:

ax² + bx + c = 0

Where:

a, b and c are real numbers and a ≠ 0.

Roots of the equation are:

For Example:

The roots of equation x² + 5x + 4 = 0 is

The roots of the equation will be imaginary if D = b² - 4ac < 0. For example - the roots of equation x² + 4x + 5 = 0 will be

Example: Calculate roots of a Quadratic equation

In the example below, a method called roots is created which takes a, b and c as arguments to calculate the roots of the equation ax² + bx + c = 0.

using System;

class MyProgram {
  static void roots(double a, double b, double c) {
    double D = b*b - 4*a*c;
    if (D >= 0) {
      double x1 = (-b + Math.Sqrt(D))/(2*a);
      double x2 = (-b - Math.Sqrt(D))/(2*a);
      Console.WriteLine("Roots are: " + x1 + ", " + x2);
    } else {
      double x1 = -b/(2*a);
      double x2 = Math.Sqrt(-D)/(2*a);
      Console.WriteLine("Roots are: " + x1 + "±" + x2 +"i");
    }
  }

  static void Main(String[] args) {
    Console.WriteLine("Equation is x*x+5x+4=0");
    roots(1,5,4);
    Console.WriteLine("\nEquation is x*x+4x+5=0");
    roots(1,4,5);
  }
}

The above code will give the following output:

Equation is x*x+5x+4=0
Roots are: -1, -4

Equation is x*x+4x+5=0
Roots are: -2±1i

C# Program - Find Roots of a Quadratic Equation

For Example:

Example: Calculate roots of a Quadratic equation

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