Quadratic Equations: Concepts and Methods

Jul 9, 2026 · 1 min read · 0 views

What is a Quadratic Equation?

A quadratic equation has the standard form ax² + bx + c = 0, where a is not zero.

Method 1: Factoring

Write the equation as a product of two brackets, then set each bracket to zero. Example: x² + 5x + 6 = 0 factors into (x + 2)(x + 3) = 0, so x = -2 or x = -3.

Method 2: The Quadratic Formula

When factoring is hard, use: x = [ -b ± √(b² - 4ac) ] / 2a.

The Discriminant

If b² - 4ac > 0: two real roots.
If b² - 4ac = 0: one real root.
If b² - 4ac < 0: no real roots.

Key Points

Always write the equation in standard form first. Check your answers by putting them back into the equation.