1. The Discriminant

2. 4x 2 + 3x + 8 = 0
What are the roots?
2
x = -b ± b - 4ac
2a
x = -3 ± 3 - 4(4)(8)
2
2(4)

3. x = -3 ± 3 2 - 4(4)(8)
2(4)
x = -3 ± -119
8

4. 2
x = -b ± b - 4ac
2a
Discriminant

5. is negative = no roots
is positive = 2 roots

6. What happens when the discriminant is 0?
=0

7. 2x 2 - 4x + 2 = 0

9. is 0 = 1 root
is negative = no roots
is positive = 2 roots