Quadratic Equation Solver | Visual Basic Sample Code

A quadratic equation is a second-degree polynomial equation in a single variable with the form:

ax² + bx + c = 0

where x represents an unknown variable, and a, b, and c are coefficients with a ≠ 0.

The solutions to the quadratic equation are given by the quadratic formula:

x = [-b ± √(b² - 4ac)] / (2a)

The expression under the square root (b² - 4ac) is called the discriminant, which determines the nature of the roots:

Positive discriminant → Two distinct real roots
Zero discriminant → One real root (repeated)
Negative discriminant → Two complex roots

Interactive Quadratic Equation Solver

Coefficient a (x²):

Coefficient b (x):

Coefficient c (constant):

Solution:

Implementation Code

Below are the Visual Basic 6 and VB.NET implementations of the quadratic equation solver:

                    Private Sub Form_Load()
    Dim a, b, c, det As Integer
    Dim root1, root2 As Single
    Dim numroot As Integer
End Sub

Private Sub new_Click()
    ' To set all values to zero
    Coeff_a.Text = ""
    Coeff_b.Text = ""
    Coeff_c.Text = ""
    Answers.Caption = ""
    txt_root1.Visible = False
    txt_root2.Visible = False
    txt_root1.Text = ""
    txt_root2.Text = ""
    Lbl_and.Visible = False
    Lbl_numroot.Caption = ""
End Sub

Private Sub Solve_Click()
    a = Val(Coeff_a.Text)
    b = Val(Coeff_b.Text)
    c = Val(Coeff_c.Text)
    
    'To compute the value of the determinant
    det = (b ^ 2) - (4 * a * c)
    
    If det > 0 Then
        Lbl_numroot.Caption = 2
        root1 = (-b + Sqr(det)) / (2 * a)
        root2 = (-b - Sqr(det)) / (2 * a)
        Answers.Caption = "The roots are "
        Lbl_and.Visible = True
        txt_root1.Visible = True
        txt_root2.Visible = True
        txt_root1.Text = Round(root1, 4)
        txt_root2.Text = Round(root2, 4)
    ElseIf det = 0 Then
        root1 = (-b) / 2 * a
        Lbl_numroot.Caption = 1
        Answers.Caption = "The root is "
        txt_root1.Visible = True
        txt_root1.Text = root1
    Else
        Lbl_numroot.Caption = 0
        Answers.Caption = "There is no root "
    End If
End Sub
                

                    Public Class QuadraticSolver
    Private Sub btnSolve_Click(sender As Object, e As EventArgs) Handles btnSolve.Click
        Dim a, b, c, discriminant, root1, root2 As Double
        
        ' Get coefficients from textboxes
        If Not Double.TryParse(txtA.Text, a) OrElse Not Double.TryParse(txtB.Text, b) _
            OrElse Not Double.TryParse(txtC.Text, c) Then
            MessageBox.Show("Please enter valid numbers")
            Return
        End If
        
        ' Check if a is zero
        If a = 0 Then
            MessageBox.Show("Coefficient a cannot be zero")
            Return
        End If
        
        ' Calculate discriminant
        discriminant = b * b - 4 * a * c
        
        ' Determine roots based on discriminant
        If discriminant > 0 Then
            ' Two real roots
            root1 = (-b + Math.Sqrt(discriminant)) / (2 * a)
            root2 = (-b - Math.Sqrt(discriminant)) / (2 * a)
            lblResult.Text = $"Two real roots: {root1:F4} and {root2:F4}"
        ElseIf discriminant = 0 Then
            ' One real root
            root1 = -b / (2 * a)
            lblResult.Text = $"One real root: {root1:F4}"
        Else
            ' Complex roots
            Dim realPart = -b / (2 * a)
            Dim imaginaryPart = Math.Sqrt(-discriminant) / (2 * a)
            lblResult.Text = $"Two complex roots: {realPart:F4} + {imaginaryPart:F4}i and {realPart:F4} - {imaginaryPart:F4}i"
        End If
    End Sub
    
    Private Sub btnClear_Click(sender As Object, e As EventArgs) Handles btnClear.Click
        ' Clear all inputs and results
        txtA.Text = ""
        txtB.Text = ""
        txtC.Text = ""
        lblResult.Text = ""
    End Sub
End Class
                

How the Quadratic Solver Works

The quadratic equation solver uses the discriminant (b² - 4ac) to determine the nature of the roots:

Discriminant Calculation

The discriminant (D = b² - 4ac) is calculated first. This value determines the number and type of roots.

Real Roots (D > 0)

When discriminant is positive, two distinct real roots exist:
x₁ = [-b + √D]/(2a)
x₂ = [-b - √D]/(2a)

Repeated Root (D = 0)

When discriminant is zero, one real root (repeated) exists:
x = -b/(2a)

Complex Roots (D < 0)

When discriminant is negative, two complex roots exist:
x = [-b ± i√|D|]/(2a)

Note: The coefficient 'a' must be non-zero for the equation to be quadratic. If a=0, the equation becomes linear.

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