Quadratic Equations Square Root Calculator

What is a Quadratic Equation Square Root?

Quadratic equations are second-degree polynomials that can be written in the standard form:

Where:

• a is the coefficient of x² (must not be zero)
• b is the coefficient of x
• c is the constant term

The square roots of a quadratic equation are the values of x that satisfy the equation. These roots can be found using the quadratic formula, which is derived from completing the square or using the discriminant.

The Formula

The quadratic formula is used to find the roots of any quadratic equation:

Where:

• √(b² - 4ac) is the discriminant
• The ± symbol indicates there are two roots
• If the discriminant is positive, there are two distinct real roots
• If the discriminant is zero, there is exactly one real root
• If the discriminant is negative, there are two complex roots

How to Use the Calculator

Using the quadratic equations square root calculator is straightforward:

1. Enter the coefficients a, b, and c in the input fields
2. Click the "Calculate" button to compute the roots
3. View the results, including the discriminant and the roots
4. Use the chart to visualize the quadratic function

The calculator will display the roots in a clear format and provide additional information about the nature of the roots based on the discriminant.

Worked Example

Let's solve the quadratic equation x² - 5x + 6 = 0 using the calculator.

1. Identify the coefficients: a = 1, b = -5, c = 6
2. Calculate the discriminant: b² - 4ac = (-5)² - 4(1)(6) = 25 - 24 = 1
3. Apply the quadratic formula:
   x = [5 ± √1] / 2
4. Find the roots:
   • x₁ = (5 + 1)/2 = 3
   • x₂ = (5 - 1)/2 = 2

The roots of the equation x² - 5x + 6 = 0 are x = 2 and x = 3.