Identify Roots Calculator

What Are Roots of a Quadratic Equation?

The roots of a quadratic equation are the values of x that satisfy the equation ax² + bx + c = 0. These roots represent the points where the parabola represented by the equation intersects the x-axis.

Quadratic equations can have:

• Two distinct real roots
• One real root (a repeated root)
• No real roots (complex roots)

The nature of the roots is determined by the discriminant (b² - 4ac).

How to Find Roots Using the Calculator

Using our identify roots calculator is simple:

1. Enter the coefficients a, b, and c from your quadratic equation
2. Click the "Calculate Roots" button
3. View the results including the roots and discriminant
4. See the graphical representation of the quadratic function

The calculator uses the quadratic formula to find the roots and provides additional information about the nature of the roots.

The Quadratic Formula

The discriminant (D) is calculated as D = b² - 4ac. The discriminant tells us about the nature of the roots:

• If D > 0: Two distinct real roots
• If D = 0: One real root (repeated)
• If D < 0: Two complex conjugate roots

Worked Example

Let's find the roots of the equation x² - 5x + 6 = 0:

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

The roots are x = 2 and x = 3.