1. The Quadratic Formula and the Discriminant
5.6
The Quadratic Formula and the Discriminant

2. The discriminant: the expression under the radical sign in the quadratic formula. *Determines what type and number of roots
Discriminant
Type and Number of Roots
b2 – 4ac > 0 is a perfect square
2 rational roots
b2 – 4ac > 0 is NOT a perfect square
2 irrational roots
b2 – 4ac = 0
1 rational root
b2 – 4ac < 0
2 complex roots

3. The Quadratic Formula:
Use when you cannot factor to find the roots/solutions

4. Use the discriminant to determine the type and number of roots, then find the exact solutions by using the Quadratic Formula
Example 1:
x2 – 3x – 40 = 0

5. Use the discriminant to determine the type and number of roots, then find the exact solutions by using the Quadratic Formula
Example 2:
2x2 – 8x + 11 = 0

6. Use the discriminant to determine the type and number of roots, then find the exact solutions by using the Quadratic Formula
Example 3:
x2 + 6x – 9 = 0

7. TOD: Solve using the method of your choice
TOD: Solve using the method of your choice! (factor or Quadratic Formula)
A. 7x2 + 3 = 0 B. 2x2 – 5x + 7 = 3
C. 2x2 - 5x – 3 = 0 D. -x2 + 2x + 7 = 0