Understanding Factoring & Quadratics

Factoring is the process of breaking down a mathematical expression into the product of other expressions. For quadratic equations in the form Ax² + Bx + C = 0, finding the factors helps identify the roots (x-intercepts) of the equation.

How This Calculator Works

This tool uses the Quadratic Formula to find the precise roots, even if they are complex numbers or irrational:

x = (-b ± √(b² - 4ac)) / 2a

The Discriminant (Δ)

The discriminant, calculated as Δ = b² - 4ac, tells us the nature of the roots:

• Positive (Δ > 0): Two distinct real roots. The graph crosses the x-axis twice.
• Zero (Δ = 0): One real root (a perfect square trinomial). The vertex touches the x-axis.
• Negative (Δ < 0): Two complex (imaginary) roots. The graph never touches the x-axis.