1. The Quadratic Formula and the Discriminant
College Algebra
1.4 (day3 Notes)

2. We have a number of different ways of finding the roots of a quadratic equation
#1. Solve by Taking Square Roots
#2. Factoring
#3. Completing the Square
Now a new way that comes from completing the square.
The Quadratic Formula

3. The Quadratic Formula
Solve for x by completing the square.

4. Yes, you can remember this formula
Pop goes the Weasel
Gilligan’s Island
This one I can’t explain

5. How does it work
Equation:

6. How does it work
Equation:

7. The Discriminant
The number in the square root of the quadratic formula.

8. The Discriminant

9. The Discriminant The Discriminant can be negative, positive or zero
If the Discriminant is positive,
there are 2 real answers.
If the Discriminant is zero,
there is 1 real answer.
If the Discriminant is negative,
there are 2 complex answers.
complex answer have i.

10. The Discriminant Discriminant Number of Solutions Type of Solutions
Positive, perfect square
(ex: 36 or 81 or 100)
Two
Real and Rational
Positive, but not a perfect square
(ex: 40, 27, 72, 91, …)
Real and Irrational
Zero
One (a double solution)
Negative
(ex: -49, -81, -5, -27, …)
Nonreal complex

11. The Discriminant
This proves that the discriminant is only useful when a, b and c are INTEGERS!!!

12. Solve using the Quadratic formula

13. Solve using the Quadratic formula

14. Solve using the Quadratic formula

15. Solve using the Quadratic formula

16. Solve using the Quadratic formula

17. Solve using the Quadratic formula

18. Solve using the Quadratic formula

19. Solve using the Quadratic formula

20. Solve using the Quadratic formula

21. Solve using the Quadratic formula

22. Solve using the Quadratic formula

23. Describe the roots
Tell me the Discriminant and the type of roots

24. Describe the roots 0, One rational root
Tell me the Discriminant and the type of roots
0, One rational root

25. Describe the roots 0, One rational root
Tell me the Discriminant and the type of roots
0, One rational root

26. Describe the roots 0, One rational root -11, Two complex roots
Tell me the Discriminant and the type of roots
0, One rational root
-11, Two complex roots

27. Describe the roots 0, One rational root -11, Two complex roots
Tell me the Discriminant and the type of roots
0, One rational root
-11, Two complex roots

28. Describe the roots 0, One rational root -11, Two complex roots
Tell me the Discriminant and the type of roots
0, One rational root
-11, Two complex roots
80, Two irrational roots

29. Homework
1.4 #72-82 even and all