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Overview
Grade 12 Advanced Functions, University Preparation (MHF4U)
C. Polynomial and Rational Functions
40. 12AF.C3.4
40.4 Nature of roots of quadratic equations: The discriminant
Nature of Roots of Quadratic Equations: The Discriminant
Discover how the discriminant formula, b squared minus 4ac, tells you whether a quadratic equation has two, one, or no real roots.
What You'll Learn
The discriminant of a quadratic equation in the form a x squared plus b x plus c equals zero is the expression b squared minus 4ac.
A positive discriminant means the equation has two distinct real roots and its graph crosses the x-axis twice.
A discriminant equal to zero means the equation has exactly one repeated real root and its graph touches the x-axis at a single point.
A negative discriminant means the equation has no real roots, only two complex roots, and its graph never touches the x-axis.
You can find the discriminant without fully solving the quadratic formula, which makes it a quick way to check the nature of roots first.
What You'll Practice
1
Computing discriminants from equations already in standard form
2
Rearranging equations to standard form before calculating the discriminant
3
Determining whether equations have two real, one real, or two complex solutions
4
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.
This Unit Includes
3 Video lessons
Learning resources
Skills
Discriminant
Quadratic Formula
Nature of Roots
Real Solutions
Complex Solutions
Standard Form
Algebra
ON Curriculum Aligned