Download presentation

Presentation is loading. Please wait.

Published byCarmel Lily Townsend Modified over 8 years ago

1
6.5 – Solving Equations with Quadratic Techniques

2
Quadratic equations are in the form: ax 2 + bx + c,

3
Quadratic equations are in the form: ax 2 + bx + c, where a, b, & c are integers

4
Quadratic equations are in the form: ax 2 + bx + c, where a, b, & c are integers exs.

5
Quadratic equations are in the form: ax 2 + bx + c, where a, b, & c are integers exs. x 2 + 5x + 2

6
Quadratic equations are in the form: ax 2 + bx + c, where a, b, & c are integers exs. x 2 + 5x + 2 2x 2 – 18x + 13

7
Quadratic equations are in the form: ax 2 + bx + c, where a, b, & c are integers exs. x 2 + 5x + 2 2x 2 – 18x + 13 x 2 – 9

8
Quadratic equations are in the form: ax 2 + bx + c, where a, b, & c are integers exs. x 2 + 5x + 2 2x 2 – 18x + 13 x 2 – 9 x 2 + 0x – 9

9
Quadratic equations are in the form: ax 2 + bx + c, where a, b, & c are integers exs. x 2 + 5x + 2 2x 2 – 18x + 13 x 2 – 9 x 2 + 0x – 9 2x 2 + 8x

10
Quadratic equations are in the form: ax 2 + bx + c, where a, b, & c are integers exs. x 2 + 5x + 2 2x 2 – 18x + 13 x 2 – 9 x 2 + 0x – 9 2x 2 + 8x 2x 2 + 8x + 0

11
Quadratic equations are in the form: ax 2 + bx + c, where a, b, & c are integers exs. x 2 + 5x + 2 2x 2 – 18x + 13 x 2 – 9 x 2 + 0x – 9 2x 2 + 8x 2x 2 + 8x + 0 NOTE: Must have the “x 2 ” term to be a quadratic!

12
Ex. 1 Write each expression in quadratic form, if possible.

13
a. x 4 + 13x 2 + 36

14
Ex. 1 Write each expression in quadratic form, if possible. a. x 4 + 13x 2 + 36 (x 2 ) 2

15
Ex. 1 Write each expression in quadratic form, if possible. a. x 4 + 13x 2 + 36 (x 2 ) 2 + 13(x 2 )

16
Ex. 1 Write each expression in quadratic form, if possible. a. x 4 + 13x 2 + 36 (x 2 ) 2 + 13(x 2 ) + 36

17
Ex. 1 Write each expression in quadratic form, if possible. a. x 4 + 13x 2 + 36 (x 2 ) 2 + 13(x 2 ) + 36

18
Ex. 1 Write each expression in quadratic form, if possible. a. x 4 + 13x 2 + 36 (x 2 ) 2 + 13(x 2 ) + 36 b. 16x 6 – 625

19
Ex. 1 Write each expression in quadratic form, if possible. a. x 4 + 13x 2 + 36 (x 2 ) 2 + 13(x 2 ) + 36 b. 16x 6 – 625 (4x 3 ) 2

20
Ex. 1 Write each expression in quadratic form, if possible. a. x 4 + 13x 2 + 36 (x 2 ) 2 + 13(x 2 ) + 36 b. 16x 6 – 625 (4x 3 ) 2 – 625

21
Ex. 1 Write each expression in quadratic form, if possible. a. x 4 + 13x 2 + 36 (x 2 ) 2 + 13(x 2 ) + 36 b. 16x 6 – 625 (4x 3 ) 2 – 625 c. x ½ – 9x ¼ + 16

22
Ex. 1 Write each expression in quadratic form, if possible. a. x 4 + 13x 2 + 36 (x 2 ) 2 + 13(x 2 ) + 36 b. 16x 6 – 625 (4x 3 ) 2 – 625 c. x ½ – 9x ¼ + 16 (x ¼ ) 2

23
Ex. 1 Write each expression in quadratic form, if possible. a. x 4 + 13x 2 + 36 (x 2 ) 2 + 13(x 2 ) + 36 b. 16x 6 – 625 (4x 3 ) 2 – 625 c. x ½ – 9x ¼ + 16 (x ¼ ) 2 – 9(x ¼ )

24
Ex. 1 Write each expression in quadratic form, if possible. a. x 4 + 13x 2 + 36 (x 2 ) 2 + 13(x 2 ) + 36 b. 16x 6 – 625 (4x 3 ) 2 – 625 c. x ½ – 9x ¼ + 16 (x ¼ ) 2 – 9(x ¼ ) + 16

25
Ex. 1 Write each expression in quadratic form, if possible. a. x 4 + 13x 2 + 36 (x 2 ) 2 + 13(x 2 ) + 36 b. 16x 6 – 625 (4x 3 ) 2 – 625 c. x ½ – 9x ¼ + 16 (x ¼ ) 2 – 9(x ¼ ) + 16

26
Ex. 2 Solve each equation. a. x 4 = 16

27
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16

28
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16 x 4 – 16 = 0

29
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16 x 4 – 16 = 0 (x 2 ) 2 – 16 = 0

30
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16 x 4 – 16 = 0 (x 2 ) 2 – 16 = 0

31
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16 x 4 – 16 = 0 (x 2 ) 2 – 16 = 0 ()() = 0

32
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16 x 4 – 16 = 0 (x 2 ) 2 – 16 = 0 ()() = 0 (x 2 )(x 2 ) = 0

33
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16 x 4 – 16 = 0 (x 2 ) 2 – 16 = 0 ()() = 0 (x 2 – 4)(x 2 + 4) = 0

34
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16 x 4 – 16 = 0 (x 2 ) 2 – 16 = 0 ()() = 0 (x 2 – 4)(x 2 + 4) = 0 x 2 – 4 = 0

35
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16 x 4 – 16 = 0 (x 2 ) 2 – 16 = 0 ()() = 0 (x 2 – 4)(x 2 + 4) = 0 x 2 – 4 = 0 OR x 2 + 4 = 0

36
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16 x 4 – 16 = 0 (x 2 ) 2 – 16 = 0 ()() = 0 (x 2 – 4)(x 2 + 4) = 0 x 2 – 4 = 0 OR x 2 + 4 = 0 ( )( ) = 0

37
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16 x 4 – 16 = 0 (x 2 ) 2 – 16 = 0 ()() = 0 (x 2 – 4)(x 2 + 4) = 0 x 2 – 4 = 0 OR x 2 + 4 = 0 ( )( ) = 0 (x )(x ) = 0

38
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16 x 4 – 16 = 0 (x 2 ) 2 – 16 = 0 ()() = 0 (x 2 – 4)(x 2 + 4) = 0 x 2 – 4 = 0 OR x 2 + 4 = 0 ( )( ) = 0 (x – 2)(x + 2) = 0

39
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16 x 4 – 16 = 0 (x 2 ) 2 – 16 = 0 ()() = 0 (x 2 – 4)(x 2 + 4) = 0 x 2 – 4 = 0 OR x 2 + 4 = 0 ( )( ) = 0 (x – 2)(x + 2) = 0 x – 2 = 0 OR x + 2 = 0

40
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16 x 4 – 16 = 0 (x 2 ) 2 – 16 = 0 ()() = 0 (x 2 – 4)(x 2 + 4) = 0 x 2 – 4 = 0 OR x 2 + 4 = 0 ( )( ) = 0 (x – 2)(x + 2) = 0 x – 2 = 0 OR x + 2 = 0 +2 +2 -2 -2

41
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16 x 4 – 16 = 0 (x 2 ) 2 – 16 = 0 ()() = 0 (x 2 – 4)(x 2 + 4) = 0 x 2 – 4 = 0 OR x 2 + 4 = 0 ( )( ) = 0 (x – 2)(x + 2) = 0 x – 2 = 0 OR x + 2 = 0 +2 +2 -2 -2 x = 2 OR x = -2

42
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16 x 4 – 16 = 0 (x 2 ) 2 – 16 = 0 ()() = 0 (x 2 – 4)(x 2 + 4) = 0 x 2 – 4 = 0 OR x 2 + 4 = 0 ( )( ) = 0 (x – 2)(x + 2) = 0 x – 2 = 0 OR x + 2 = 0 +2 +2 -2 -2 x = 2 OR x = -2

43
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16 x 4 – 16 = 0 (x 2 ) 2 – 16 = 0 ()() = 0 (x 2 – 4)(x 2 + 4) = 0 x 2 – 4 = 0 OR x 2 + 4 = 0 ( )( ) = 0 OR ( )( ) = 0 (x – 2)(x + 2) = 0 x – 2 = 0 OR x + 2 = 0 +2 +2 -2 -2 x = 2 OR x = -2

44
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16 x 4 – 16 = 0 (x 2 ) 2 – 16 = 0 ()() = 0 (x 2 – 4)(x 2 + 4) = 0 x 2 – 4 = 0 OR x 2 + 4 = 0 ( )( ) = 0 OR ( )( ) = 0 (x – 2)(x + 2) = 0 OR x 2 + 4 = 0 x – 2 = 0 OR x + 2 = 0 +2 +2 -2 -2 x = 2 OR x = -2

45
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16 x 4 – 16 = 0 (x 2 ) 2 – 16 = 0 ()() = 0 (x 2 – 4)(x 2 + 4) = 0 x 2 – 4 = 0 OR x 2 + 4 = 0 ( )( ) = 0 OR ( )( ) = 0 (x – 2)(x + 2) = 0 OR x 2 + 4 = 0 x – 2 = 0 OR x + 2 = 0 OR x 2 = -4 +2 +2 -2 -2 x = 2 OR x = -2

46
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16 x 4 – 16 = 0 (x 2 ) 2 – 16 = 0 ()() = 0 (x 2 – 4)(x 2 + 4) = 0 x 2 – 4 = 0 OR x 2 + 4 = 0 ( )( ) = 0 OR ( )( ) = 0 (x – 2)(x + 2) = 0 OR x 2 + 4 = 0 x – 2 = 0 OR x + 2 = 0 OR x 2 = -4 +2 +2 -2 -2 √x 2 = √-4 x = 2 OR x = -2

47
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16 x 4 – 16 = 0 (x 2 ) 2 – 16 = 0 ()() = 0 (x 2 – 4)(x 2 + 4) = 0 x 2 – 4 = 0 OR x 2 + 4 = 0 ( )( ) = 0 OR ( )( ) = 0 (x – 2)(x + 2) = 0 OR x 2 + 4 = 0 x – 2 = 0 OR x + 2 = 0 OR x 2 = -4 +2 +2 -2 -2 √x 2 = √-4 x = 2 OR x = -2 OR x = ±2i

48
Ex. 2 Solve each equation. a. x 4 = 16 -16 -16 x 4 – 16 = 0 (x 2 ) 2 – 16 = 0 ()() = 0 (x 2 – 4)(x 2 + 4) = 0 x 2 – 4 = 0 OR x 2 + 4 = 0 ( )( ) = 0 OR ( )( ) = 0 (x – 2)(x + 2) = 0 OR x 2 + 4 = 0 x – 2 = 0 OR x + 2 = 0 OR x 2 = -4 +2 +2 -2 -2 √x 2 = √-4 x = 2 OR x = -2 OR x = ±2i

49
b. x 4 + 11x 2 + 18 = 0

51
(x 2 ) 2 + 11(x 2 ) + 18 = 0

52
b. x 4 + 11x 2 + 18 = 0 (x 2 ) 2 + 11(x 2 ) + 18 = 0 ()() = 0

53
b. x 4 + 11x 2 + 18 = 0 (x 2 ) 2 + 11(x 2 ) + 18 = 0 ()() = 0 (x 2 )(x 2 ) = 0

54
b. x 4 + 11x 2 + 18 = 0 (x 2 ) 2 + 11(x 2 ) + 18 = 0 ()() = 0 (x 2 + 9)(x 2 + 2) = 0

55
b. x 4 + 11x 2 + 18 = 0 (x 2 ) 2 + 11(x 2 ) + 18 = 0 ()() = 0 (x 2 + 9)(x 2 + 2) = 0 x 2 + 9 = 0

56
b. x 4 + 11x 2 + 18 = 0 (x 2 ) 2 + 11(x 2 ) + 18 = 0 ()() = 0 (x 2 + 9)(x 2 + 2) = 0 x 2 + 9 = 0 OR x 2 + 2 = 0

57
b. x 4 + 11x 2 + 18 = 0 (x 2 ) 2 + 11(x 2 ) + 18 = 0 ()() = 0 (x 2 + 9)(x 2 + 2) = 0 x 2 + 9 = 0 OR x 2 + 2 = 0

58
b. x 4 + 11x 2 + 18 = 0 (x 2 ) 2 + 11(x 2 ) + 18 = 0 ()() = 0 (x 2 + 9)(x 2 + 2) = 0 x 2 + 9 = 0 OR x 2 + 2 = 0 ( )( ) = 0

59
b. x 4 + 11x 2 + 18 = 0 (x 2 ) 2 + 11(x 2 ) + 18 = 0 ()() = 0 (x 2 + 9)(x 2 + 2) = 0 x 2 + 9 = 0 OR x 2 + 2 = 0 (x + )(x + ) = 0

60
b. x 4 + 11x 2 + 18 = 0 (x 2 ) 2 + 11(x 2 ) + 18 = 0 ()() = 0 (x 2 + 9)(x 2 + 2) = 0 x 2 + 9 = 0 OR x 2 + 2 = 0 ( )( ) = 0 x 2 + 9 = 0

61
b. x 4 + 11x 2 + 18 = 0 (x 2 ) 2 + 11(x 2 ) + 18 = 0 ()() = 0 (x 2 + 9)(x 2 + 2) = 0 x 2 + 9 = 0 OR x 2 + 2 = 0 ( )( ) = 0 ()() = 0 x 2 + 9 = 0 -9 -9

62
b. x 4 + 11x 2 + 18 = 0 (x 2 ) 2 + 11(x 2 ) + 18 = 0 ()() = 0 (x 2 + 9)(x 2 + 2) = 0 x 2 + 9 = 0 OR x 2 + 2 = 0 ( )( ) = 0 ()() = 0 x 2 + 9 = 0 -9 -9 x 2 = -9

63
b. x 4 + 11x 2 + 18 = 0 (x 2 ) 2 + 11(x 2 ) + 18 = 0 ()() = 0 (x 2 + 9)(x 2 + 2) = 0 x 2 + 9 = 0 OR x 2 + 2 = 0 ( )( ) = 0 ()() = 0 x 2 + 9 = 0 -9 -9 x 2 = -9 √x 2 = √-9

64
b. x 4 + 11x 2 + 18 = 0 (x 2 ) 2 + 11(x 2 ) + 18 = 0 ()() = 0 (x 2 + 9)(x 2 + 2) = 0 x 2 + 9 = 0 OR x 2 + 2 = 0 ( )( ) = 0 ()() = 0 x 2 + 9 = 0 -9 -9 x 2 = -9 √x 2 = √-9 x = ±3i

65
b. x 4 + 11x 2 + 18 = 0 (x 2 ) 2 + 11(x 2 ) + 18 = 0 ()() = 0 (x 2 + 9)(x 2 + 2) = 0 x 2 + 9 = 0 OR x 2 + 2 = 0 ( )( ) = 0 ()() = 0 x 2 + 9 = 0 -9 -9 x 2 = -9 √x 2 = √-9 x = ±3i

66
b. x 4 + 11x 2 + 18 = 0 (x 2 ) 2 + 11(x 2 ) + 18 = 0 ()() = 0 (x 2 + 9)(x 2 + 2) = 0 x 2 + 9 = 0 OR x 2 + 2 = 0 ( )( ) = 0 (x +)(x + ) = 0 x 2 + 9 = 0 -9 -9 x 2 = -9 √x 2 = √-9 x = ±3i

67
b. x 4 + 11x 2 + 18 = 0 (x 2 ) 2 + 11(x 2 ) + 18 = 0 ()() = 0 (x 2 + 9)(x 2 + 2) = 0 x 2 + 9 = 0 OR x 2 + 2 = 0 ( )( ) = 0 ()() = 0 x 2 + 9 = 0 OR x 2 + 2 = 0 -9 -9 x 2 = -9 √x 2 = √-9 x = ±3i

68
b. x 4 + 11x 2 + 18 = 0 (x 2 ) 2 + 11(x 2 ) + 18 = 0 ()() = 0 (x 2 + 9)(x 2 + 2) = 0 x 2 + 9 = 0 OR x 2 + 2 = 0 ( )( ) = 0 ()() = 0 x 2 + 9 = 0 OR x 2 + 2 = 0 -9 -9 -2 -2 x 2 = -9 √x 2 = √-9 x = ±3i

69
b. x 4 + 11x 2 + 18 = 0 (x 2 ) 2 + 11(x 2 ) + 18 = 0 ()() = 0 (x 2 + 9)(x 2 + 2) = 0 x 2 + 9 = 0 OR x 2 + 2 = 0 ( )( ) = 0 ()() = 0 x 2 + 9 = 0 OR x 2 + 2 = 0 -9 -9 -2 -2 x 2 = -9 OR x 2 = -2 √x 2 = √-9 x = ±3i

70
b. x 4 + 11x 2 + 18 = 0 (x 2 ) 2 + 11(x 2 ) + 18 = 0 ()() = 0 (x 2 + 9)(x 2 + 2) = 0 x 2 + 9 = 0 OR x 2 + 2 = 0 ( )( ) = 0 ()() = 0 x 2 + 9 = 0 OR x 2 + 2 = 0 -9 -9 -2 -2 x 2 = -9 OR x 2 = -2 √x 2 = √-9 OR √x 2 = √-2 x = ±3i

71
b. x 4 + 11x 2 + 18 = 0 (x 2 ) 2 + 11(x 2 ) + 18 = 0 ()() = 0 (x 2 + 9)(x 2 + 2) = 0 x 2 + 9 = 0 OR x 2 + 2 = 0 ( )( ) = 0 ()() = 0 x 2 + 9 = 0 OR x 2 + 2 = 0 -9 -9 -2 -2 x 2 = -9 OR x 2 = -2 √x 2 = √-9 OR √x 2 = √-2 x = ±3i OR x = ±i√2

72
b. x 4 + 11x 2 + 18 = 0 (x 2 ) 2 + 11(x 2 ) + 18 = 0 ()() = 0 (x 2 + 9)(x 2 + 2) = 0 x 2 + 9 = 0 OR x 2 + 2 = 0 ( )( ) = 0 ()() = 0 x 2 + 9 = 0 OR x 2 + 2 = 0 -9 -9 -2 -2 x 2 = -9 OR x 2 = -2 √x 2 = √-9 OR √x 2 = √-2 x = ±3i OR x = ±i√2

73
c. x ½ – 6x ¼ – 16 = 0

75
(x ¼ ) 2 – 6(x ¼ ) – 16 = 0

76
c. x ½ – 6x ¼ – 16 = 0 (x ¼ ) 2 – 6(x ¼ ) – 16 = 0 ()() = 0

77
c. x ½ – 6x ¼ – 16 = 0 (x ¼ ) 2 – 6(x ¼ ) – 16 = 0 ()() = 0 (x ¼ )(x ¼ ) = 0

78
c. x ½ – 6x ¼ – 16 = 0 (x ¼ ) 2 – 6(x ¼ ) – 16 = 0 ()() = 0 (x ¼ – 8)(x ¼ + 2) = 0

79
c. x ½ – 6x ¼ – 16 = 0 (x ¼ ) 2 – 6(x ¼ ) – 16 = 0 ()() = 0 (x ¼ – 8)(x ¼ + 2) = 0 x ¼ – 8 = 0

80
c. x ½ – 6x ¼ – 16 = 0 (x ¼ ) 2 – 6(x ¼ ) – 16 = 0 ()() = 0 (x ¼ – 8)(x ¼ + 2) = 0 x ¼ – 8 = 0 OR x ¼ + 2 = 0

81
c. x ½ – 6x ¼ – 16 = 0 (x ¼ ) 2 – 6(x ¼ ) – 16 = 0 ()() = 0 (x ¼ – 8)(x ¼ + 2) = 0 x ¼ – 8 = 0 OR x ¼ + 2 = 0 ( )( ) = 0

82
c. x ½ – 6x ¼ – 16 = 0 (x ¼ ) 2 – 6(x ¼ ) – 16 = 0 ()() = 0 (x ¼ – 8)(x ¼ + 2) = 0 x ¼ – 8 = 0 OR x ¼ + 2 = 0 ( )( ) = 0 x ¼ – 8 = 0

83
c. x ½ – 6x ¼ – 16 = 0 (x ¼ ) 2 – 6(x ¼ ) – 16 = 0 ()() = 0 (x ¼ – 8)(x ¼ + 2) = 0 x ¼ – 8 = 0 OR x ¼ + 2 = 0 ( )( ) = 0 x ¼ – 8 = 0 +8 +8

84
c. x ½ – 6x ¼ – 16 = 0 (x ¼ ) 2 – 6(x ¼ ) – 16 = 0 ()() = 0 (x ¼ – 8)(x ¼ + 2) = 0 x ¼ – 8 = 0 OR x ¼ + 2 = 0 ( )( ) = 0 x ¼ – 8 = 0 +8 +8 x ¼ = 8

85
c. x ½ – 6x ¼ – 16 = 0 (x ¼ ) 2 – 6(x ¼ ) – 16 = 0 ()() = 0 (x ¼ – 8)(x ¼ + 2) = 0 x ¼ – 8 = 0 OR x ¼ + 2 = 0 ( )( ) = 0 x ¼ – 8 = 0 +8 +8 x ¼ = 8 (x ¼ ) 4 = (8) 4

86
c. x ½ – 6x ¼ – 16 = 0 (x ¼ ) 2 – 6(x ¼ ) – 16 = 0 ()() = 0 (x ¼ – 8)(x ¼ + 2) = 0 x ¼ – 8 = 0 OR x ¼ + 2 = 0 ( )( ) = 0 x ¼ – 8 = 0 +8 +8 x ¼ = 8 (x ¼ ) 4 = (8) 4 x = 4096

87
c. x ½ – 6x ¼ – 16 = 0 (x ¼ ) 2 – 6(x ¼ ) – 16 = 0 ()() = 0 (x ¼ – 8)(x ¼ + 2) = 0 x ¼ – 8 = 0 OR x ¼ + 2 = 0 ( )( ) = 0 x ¼ – 8 = 0 +8 +8 x ¼ = 8 (x ¼ ) 4 = (8) 4 x = 4096

88
c. x ½ – 6x ¼ – 16 = 0 (x ¼ ) 2 – 6(x ¼ ) – 16 = 0 ()() = 0 (x ¼ – 8)(x ¼ + 2) = 0 x ¼ – 8 = 0 OR x ¼ + 2 = 0 ( )( ) = 0 ()( ) = 0 x ¼ – 8 = 0 +8 +8 x ¼ = 8 (x ¼ ) 4 = (8) 4 x = 4096

89
c. x ½ – 6x ¼ – 16 = 0 (x ¼ ) 2 – 6(x ¼ ) – 16 = 0 ()() = 0 (x ¼ – 8)(x ¼ + 2) = 0 x ¼ – 8 = 0 OR x ¼ + 2 = 0 ( )( ) = 0 ()( ) = 0 x ¼ – 8 = 0 OR x ¼ + 2 = 0 +8 +8 x ¼ = 8 (x ¼ ) 4 = (8) 4 x = 4096

90
c. x ½ – 6x ¼ – 16 = 0 (x ¼ ) 2 – 6(x ¼ ) – 16 = 0 ()() = 0 (x ¼ – 8)(x ¼ + 2) = 0 x ¼ – 8 = 0 OR x ¼ + 2 = 0 ( )( ) = 0 ()( ) = 0 x ¼ – 8 = 0 OR x ¼ + 2 = 0 +8 +8 -2 -2 x ¼ = 8 (x ¼ ) 4 = (8) 4 x = 4096

91
c. x ½ – 6x ¼ – 16 = 0 (x ¼ ) 2 – 6(x ¼ ) – 16 = 0 ()() = 0 (x ¼ – 8)(x ¼ + 2) = 0 x ¼ – 8 = 0 OR x ¼ + 2 = 0 ( )( ) = 0 ()( ) = 0 x ¼ – 8 = 0 OR x ¼ + 2 = 0 +8 +8 -2 -2 x ¼ = 8 OR x ¼ = -2 (x ¼ ) 4 = (8) 4 x = 4096

92
c. x ½ – 6x ¼ – 16 = 0 (x ¼ ) 2 – 6(x ¼ ) – 16 = 0 ()() = 0 (x ¼ – 8)(x ¼ + 2) = 0 x ¼ – 8 = 0 OR x ¼ + 2 = 0 ( )( ) = 0 ()( ) = 0 x ¼ – 8 = 0 OR x ¼ + 2 = 0 +8 +8 -2 -2 x ¼ = 8 OR x ¼ = -2 (x ¼ ) 4 = (8) 4 OR (x ¼ ) 4 = (-2) 4 x = 4096

93
c. x ½ – 6x ¼ – 16 = 0 (x ¼ ) 2 – 6(x ¼ ) – 16 = 0 ()() = 0 (x ¼ – 8)(x ¼ + 2) = 0 x ¼ – 8 = 0 OR x ¼ + 2 = 0 ( )( ) = 0 ()( ) = 0 x ¼ – 8 = 0 OR x ¼ + 2 = 0 +8 +8 -2 -2 x ¼ = 8 OR x ¼ = -2 (x ¼ ) 4 = (8) 4 OR (x ¼ ) 4 = (-2) 4 x = 4096 OR x = 16

94
c. x ½ – 6x ¼ – 16 = 0 (x ¼ ) 2 – 6(x ¼ ) – 16 = 0 ()() = 0 (x ¼ – 8)(x ¼ + 2) = 0 x ¼ – 8 = 0 OR x ¼ + 2 = 0 ( )( ) = 0 ()( ) = 0 x ¼ – 8 = 0 OR x ¼ + 2 = 0 +8 +8 -2 -2 x ¼ = 8 OR x ¼ = -2 (x ¼ ) 4 = (8) 4 OR (x ¼ ) 4 = (-2) 4 x = 4096 OR x = 16

Similar presentations

© 2023 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google