Nature of roots of quadratic equations: The discriminant

What You'll Learn

Identify the discriminant as the expression b² - 4ac from the quadratic formula

Calculate the discriminant by substituting a, b, and c values from quadratic equations

Determine the nature of roots based on whether the discriminant is positive, zero, or negative

Recognize that discriminant > 0 means two real solutions, = 0 means one real solution, < 0 means two complex solutions

Rearrange quadratic equations into standard form ax² + bx + c = 0 before finding the discriminant

What You'll Practice

Computing discriminants from equations already in standard form

Rearranging equations to standard form before calculating the discriminant

Determining whether equations have two real, one real, or two complex solutions

Evaluating discriminants with negative coefficients and squaring operations

Why This Matters

The discriminant helps you quickly analyze quadratic equations without solving them completely. This skill is essential in advanced algebra, calculus, and physics where you need to determine solution types efficiently. It's a powerful shortcut that saves time on tests and real-world problem-solving.

Before You Start — Make Sure You Can:

Quadratic function in general form: y = ax^2 + bx + cSolving quadratic equations using the quadratic formula Shortcut: Vertex formula Multiplying and dividing radicals

This Unit Includes

3 Video lessons

Skills

Discriminant

Quadratic Formula

Nature of Roots

Real Solutions

Complex Solutions

Standard Form

Algebra

OH Curriculum Aligned