1. Quadratic Formula & Discriminant

2. Discriminant The Discriminant
In the quadratic formula, the expression underneath the radical that describes the nature of the roots.

3. Understanding the discriminant
# of real roots
2 real roots
1 real root
No real roots
2 Imaginary Roots

4. Example 1

5. Example 2
2 Complex or Imaginary Roots!

6. Using the discriminant Put in Correct Order First!!

7. Try This One Yourself!

8. Try This 1, 2!

9. Recap Of All Three Types
9x2+6x-4=0
a=9, b=6, c=-4
b2-4ac=(6)2-4(9)(-4)
=36+144=180
2 real solutions
c. 9x2+6x+5=0
a=9, b=6, c=5
b2-4ac=(6)2-4(9)(5)
=36-180=-144
2 imaginary solutions
Find the discriminant and give the number and type of solutions.
9x2+6x+1=0
a=9, b=6, c=1
b2-4ac=(6)2-4(9)(1)
=36-36=0
1 real solution

10. Assignment
Quiz:
Homework: