Discriminant
b²−4ac tells the number and type of roots.
Key idea
b²−4ac tells the number and type of roots.
In depth
D = b² − 4ac is the part under the square root. If D > 0 there are two real roots, D = 0 gives one repeated root, D < 0 gives no real roots (two complex ones). It tells you how many times the parabola crosses the x-axis.
Worked example
x² + 2x + 5: D = 4 − 20 = −16, so no real roots.
Formula
Real-world uses
- Checking whether a bridge or projectile path reaches a height before solving
- Classifying conic sections
Common mistake
Forgetting that D is computed before the square root is taken.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Discriminant?
b²−4ac tells the number and type of roots. It is a topic at the advanced level in Algebra.
What is the formula for Discriminant?
The key formula is Δ = b² − 4ac.
Where is Discriminant used in real life?
Real-world examples: Checking whether a bridge or projectile path reaches a height before solving; Classifying conic sections.
What should I learn before Discriminant?
Make sure you are comfortable with Quadratic Formula, the previous topic in Algebra.
What is a common mistake with Discriminant?
Forgetting that D is computed before the square root is taken.
How can I practise Discriminant?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Discriminant?
Move on to Parabolas and Vertex Form next.
Related advanced topics in Algebra
- Absolute Value Inequalities – Rewrite as a compound inequality.
- Systems with Three Variables – Reduce to two variables then solve in sequence.
- Systems of Inequalities – Solution region is the overlap of half-planes.
- Factoring by Grouping – Group terms in pairs to find a common binomial.
- Sum and Difference of Cubes – Special factoring patterns for cubes.
- Completing the Square – Rewrite a quadratic as a perfect square plus constant.