Programming a quadratic equation solver in Visual Basic (VB.NET) involves taking the standard quadratic formula:

(-b±√(b²-4ac))/(2a)

and converting it into code. Here’s a basic guide on how to create a quadratic equation solver in VB.NET:

**Setup a New Project**:- Open Visual Studio and create a new VB.NET Windows Forms App project.
- Design a simple form with three TextBox controls (for a, b, and c coefficients), two Label controls (to display the results), and a Button control (to trigger the calculation).

**Write the Code**: Double-click the Button control to create its Click event handler and enter the following code:

`Private Sub btnSolve_Click(sender As Object, e As EventArgs) Handles btnSolve.Click`

' Declare variables for the coefficients and solutions

Dim a As Double, b As Double, c As Double

Dim discriminant As Double, root1 As Double, root2 As Double

`' Get coefficients from TextBoxes`

a = Double.Parse(txtA.Text)

b = Double.Parse(txtB.Text)

c = Double.Parse(txtC.Text)

`' Calculate the discriminant`

discriminant = b * b - 4 * a * c

`If discriminant > 0 Then`

' Two real and distinct roots

root1 = (-b + Math.Sqrt(discriminant)) / (2 * a)

root2 = (-b - Math.Sqrt(discriminant)) / (2 * a)

lblResult1.Text = "Root 1: " & root1.ToString()

lblResult2.Text = "Root 2: " & root2.ToString()

ElseIf discriminant = 0 Then

' Exactly one real root

root1 = -b / (2 * a)

lblResult1.Text = "Root: " & root1.ToString()

lblResult2.Text = "Only one real root exists."

Else

' No real roots (complex roots)

lblResult1.Text = "No real roots exist."

lblResult2.Text = ""

End If

End Sub

**Run the Program**:- Build and run the program.
- Input the coefficients for a, b, and c, and click the button to see the roots.

This is a simple example. If you want a more user-friendly application, consider adding error handling (to deal with non-numeric inputs or cases where `a`

is 0) and enhancing the UI to make it clearer and more intuitive.