Cogito
Algebra 1 · Chapter 8 · Lesson 3
The Discriminant
How many real roots, before solving.
11 problems · about 22 minutes · A-REI.B.4
What this lesson teaches
The student uses the discriminant to count real roots.
- The discriminant is b² − 4ac, the part under the root.
- Positive gives two roots, zero gives one, negative gives none.
- It answers how many before any solving is done.
Warm Up
Straightforward practice. Get the method working first.
4 problemsa = 1, b = 2, c = 1. Discriminant?
Answer 0
Why 0.
a = 1, b = 4, c = 4. Discriminant?
Answer 0
Why 16 − 16.
Discriminant 0. How many real roots?
Answer 1
Why A repeated root.
a = 1, b = 1, c = 5. Discriminant?
Answer -19
Why 1 − 20.
Build It Up
The same ideas with more to keep track of.
3 problemsDiscriminant −19. How many real roots?
Answer 0
Why Negative.
a = 2, b = 5, c = 2. Discriminant?
Answer 9
Why 25 − 16.
Sort each discriminant by the number of real roots it gives.
Answer Two roots: Positive · One root: Zero · No real roots: Negative
Why Think about what is under the square root.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsA parabola touching the axis exactly once. Discriminant?
Answer 0
Why A repeated root.
a = 1, b = 0, c = −9. Discriminant?
Answer 36
Why 0 + 36.
The Value: a = 1, b = 6, c = 5. What is the discriminant?
Answer 16
Why 16.
The Count: Discriminant 16. How many real roots?
Answer 2
Why Two.