## Introduction

Hello, and welcome to my small article about Quadratic Equations.

## Quadratic Equations

In algebra, a *quadratic equation* is any equation in the form of *ax ^{2} + bx + c = 0*. In the previous expression, x represents an unknown, and a, b, and c represent known numbers such that a is not equal to 0. The numbers a, b, and c are the

*coefficients*of the equation, and can be distinguished by calling them the quadratic coefficient, the linear coefficient, and the constant or free term.

## Our Project

Use Visual Studio to create either a VB.NET or a C# Windows Forms Application and design the form to resemble Figure 1.

**Figure 1:** Design

Please note that my naming of objects may be different than yours.

## Code

Add the following namespaces to your code:

**C#**

using System; using System.Windows.Forms;

**VB.NET**

Imports System.Math

Add the following fields to your form.

**C#**

private double sngCoEffA; private double sngCoEffB; private double sngCoEffC; private double sngDiscriminant; private double sngRoot1; private double sngRoot2;

**VB.NET**

Private sngCoEffA As Double Private sngCoEffB As Double Private sngCoEffC As Double Private sngDiscriminant As Double Private sngRoot1 As Double Private sngRoot2 As Double

In the preceding code, you have created the *Coefficient* objects, *Discriminant* objects, as well as the *Root* objects. Add the following code for the **Calculate** button.

**C#**

private void btnCalculate_Click(object sender, EventArgs e) { sngCoEffA = float.Parse(txtCoEfficient1.Text.ToString()); sngCoEffB = float.Parse(txtCoEfficient2.Text.ToString()); sngCoEffC = float.Parse(txtCoEfficient3.Text.ToString()); sngDiscriminant = (sngCoEffB * sngCoEffB) - (4 * sngCoEffA * sngCoEffC); if ((sngDiscriminant > 0)) { sngRoot1 = (-sngCoEffB + Math.Sqrt(sngDiscriminant)) / (2 * sngCoEffA); sngRoot2 = (-sngCoEffB - Math.Sqrt(sngDiscriminant)) / (2 * sngCoEffA); txtRoot1.Text = sngRoot1.ToString(); txtRoot2.Text = sngRoot2.ToString(); } else if ((sngDiscriminant == 0)) { sngRoot1 = (-sngCoEffB + Math.Sqrt(sngDiscriminant)) / (2 * sngCoEffA); MessageBox.Show("One Root"); txtRoot1.Text = sngRoot1.ToString(); } else { MessageBox.Show("No Root"); } }

**VB.NET**

Private Sub btnCalculate_Click(ByVal sender As System.Object, _ ByVal e As System.EventArgs) Handles btnCalculate.Click sngCoEffA = txtCoEfficient1.Text sngCoEffB = txtCoEfficient2.Text sngCoEffC = txtCoEfficient3.Text sngDiscriminant = (sngCoEffB * sngCoEffB) - (4 * sngCoEffA _ * sngCoEffC) If (sngDiscriminant > 0) Then sngRoot1 = (-sngCoEffB + Math.Sqrt(sngDiscriminant)) / _ (2 * sngCoEffA) sngRoot2 = (-sngCoEffB - Math.Sqrt(sngDiscriminant)) / _ (2 * sngCoEffA) txtRoot1.Text = sngRoot1 txtRoot2.Text = sngRoot2 ElseIf (sngDiscriminant = 0) Then sngRoot1 = (-sngCoEffB + Math.Sqrt(sngDiscriminant)) / _ (2 * sngCoEffA) MessageBox.Show("One Root") txtRoot1.Text = sngRoot1 Else MessageBox.Show("No Root") End If End Sub

The code for the calculate button works out the **Quadratic Equation** based on the values that were input. When run, the Form might resemble Figure 2.

**Figure 2:** Running

## Conclusion

Quadratic Equations might seem scary and daunting, especially when complicated formulas are involved. Hopefully, in a follow-up article I can explain a different technique. Until then, happy coding!