1. The
QUADRATIC
Discriminant

2. Quadratic Equation
Quadratic Formula

3. Quadratic Formula

4. Two Solutions or

5. ROOTS

7. Discriminant D

8. Discriminant D

11. PROBLEM #1

12. QUADRATIC
FORMULA
Double Root
Roots

13. D =
Problem #1 ?
Double Root

14. D =
Problem #1
Double Root
ONE REAL DOUBLE ROOT

15. Summary
D =
Problem #1
Double Root
ONE REAL DOUBLE ROOT

16. Could you have factored?
YES

17. PROBLEM #2

18. QUADRATIC
FORMULA
Roots

19. D =
Problem #2 ?

20. 36 D = Problem #2 TWO Unequal REAL ROOTS Unequal Rationals
PerfectSquare 36
Problem #2
Unequal Rationals
TWO Unequal REAL ROOTS

21. D = 36 Problem #2 TWO Unequal REAL ROOTS Unequal Rationals
PerfectSquare
Problem #2 36
Unequal Rationals
TWO Unequal REAL ROOTS

22. What's a Rational Number?

23. What's a Rational Number?

24. What's a Rational Number?

25. What's a Rational Number?

26. What's a Rational Number?

27. What's a Rational Number?

28. What's a Rational Number?

29. What's a Rational Number?

30. D = 36 Problem #2 TWO Unequal REAL ROOTS Unequal Rationals
PerfectSquare
Problem #2 36
Unequal Rationals
TWO Unequal REAL ROOTS

31. D = 36 Summary Problem #2 TWO Unequal REAL ROOTS Unequal Rationals
PerfectSquare
Problem #2 36
Unequal Rationals
TWO Unequal REAL ROOTS

32. Could you have factored?
YES

33. PROBLEM #3

34. QUADRATIC
FORMULA
Roots

35. D =
Problem #3 ?

36. Irrational Conjugates
NOT A Perfect Square
D = 8
Problem #3
TWO Unequal REAL ROOTS
Irrational Conjugates

37. Irrational Conjugates
NOT A Perfect Square
D =
Problem #3 8
TWO Unequal REAL ROOTS
Irrational Conjugates

38. What's an Irrational Number?

39. What's an Irrational Number?
What are Irrational Conjugates?
and

40. What's an Irrational Number?
What are Irrational Conjugates?
and

41. Irrational Conjugates
NOT A Perfect Square
D =
Problem #3 8
TWO Unequal REAL ROOTS
Irrational Conjugates

42. Irrational Conjugates
Summary
NOT A Perfect Square
D =
Problem #3 8
TWO Unequal REAL ROOTS
Irrational Conjugates

43. Could you have factored?NO
Must use the Quadratic Formula or Completing the Square to Solve

44. PROBLEM #4

45. QUADRATIC
FORMULA
Roots

46. D =
Problem #4 ?

47. TWO Unequal IMAGINARY ROOTS
D = -8
Problem #4
Negative
Imaginary Conjugates
TWO Unequal IMAGINARY ROOTS

48. TWO Unequal IMAGINARY ROOTS
D =
Problem #4 -8
Negative
Imaginary Conjugates
TWO Unequal IMAGINARY ROOTS

49. What are Imaginary Conjugates?
and

50. What are Imaginary Conjugates?
and

51. What are Imaginary Conjugates?
and
Real Part ?

52. What are Imaginary Conjugates?
and
Imaginary Part ?

53. TWO Unequal IMAGINARY ROOTS
D =
Problem #4 -8
Negative
Imaginary Conjugates
TWO Unequal IMAGINARY ROOTS

54. TWO Unequal IMAGINARY ROOTS
Summary
D =
Problem #4 -8
Negative
TWO Unequal IMAGINARY ROOTS
Imaginary Conjugates

55. Could you have factored?NO
Must use the Quadratic Formula or Completing the Square to Solve

56. Summary of
All Types

57. What are the possibilities
DISCRIMINANT
What are the possibilities
for any number?

58. DISCRIMINANT

59. DISCRIMINANT

60. DISCRIMINANT

61. TWO IMAGINARY CONJUGATE ROOTS
DISCRIMINANT
TWO IMAGINARY CONJUGATE ROOTS

62. TWO IMAGINARY CONJUGATE ROOTS
DISCRIMINANT
TWO IMAGINARY CONJUGATE ROOTS
ONE REAL DOUBLE ROOT ?

63. ONE REAL DOUBLE ROOT

64. TWO IMAGINARY CONJUGATE ROOTS
DISCRIMINANT
TWO IMAGINARY CONJUGATE ROOTS
ONE REAL DOUBLE ROOT

65. TWO IMAGINARY CONJUGATE ROOTS
DISCRIMINANT
TWO UNEQUAL REAL ROOTS
TWO IMAGINARY CONJUGATE ROOTS
ONE REAL DOUBLE ROOT

66. TWO IMAGINARY CONJUGATE ROOTS
DISCRIMINANT
TWO UNEQUAL REAL ROOTS
TWO IMAGINARY CONJUGATE ROOTS
ONE REAL DOUBLE ROOT
Perfect Square
Not A Perfect Square ?

67. TWO IMAGINARY CONJUGATE ROOTS
DISCRIMINANT
TWO UNEQUAL REAL ROOTS
TWO IMAGINARY CONJUGATE ROOTS
ONE REAL DOUBLE ROOT
Perfect Square
Not A Perfect Square
Two Unequal Rationals ?

68. TWO IMAGINARY CONJUGATE ROOTS Two Unequal Irrational Conjugates
DISCRIMINANT
TWO UNEQUAL REAL ROOTS
TWO IMAGINARY CONJUGATE ROOTS
ONE REAL DOUBLE ROOT
Perfect Square
Not A Perfect Square
Two Unequal Rationals
Two Unequal Irrational Conjugates

69. TWO IMAGINARY CONJUGATE ROOTS Two Unequal Irrational Conjugates
DISCRIMINANT
TWO UNEQUAL REAL ROOTS
TWO IMAGINARY CONJUGATE ROOTS
ONE REAL DOUBLE ROOT
Perfect Square
Not A Perfect Square
Two Unequal Rationals
Two Unequal Irrational Conjugates

70. TWO IMAGINARY CONJUGATE ROOTS Two Unequal Irrational Conjugates
Which Ones Can You Solve by Factoring
DISCRIMINANT
TWO UNEQUAL REAL ROOTS
TWO IMAGINARY CONJUGATE ROOTS
ONE REAL DOUBLE ROOT
Factor ? ?
Perfect Square
Not A Perfect Square
Factor
Two Unequal Rationals
Two Unequal Irrational Conjugates ? ?

71. TWO IMAGINARY CONJUGATE ROOTS Two Unequal Irrational Conjugates
Which Ones MUST You Solve by The Quadratic Formula or Completing The Square
DISCRIMINANT
TWO UNEQUAL REAL ROOTS
TWO IMAGINARY CONJUGATE ROOTS
ONE REAL DOUBLE ROOT
Factor ?
FORMULA ?
FORMULA
Perfect Square
Not A Perfect Square
Factor
or Complete
The Square
Two Unequal Rationals
Two Unequal Irrational Conjugates ? ?
or Complete
The Square

72. TWO IMAGINARY CONJUGATE ROOTS Two Unequal Irrational Conjugates
DISCRIMINANT
TWO UNEQUAL REAL ROOTS
TWO IMAGINARY CONJUGATE ROOTS
ONE REAL DOUBLE ROOT
Perfect Square
Not A Perfect Square
Two Unequal Rationals
Two Unequal Irrational Conjugates