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Algebra 2: Section 5.6Algebra 2: Section 5.6
The Quadratic Formula The Quadratic Formula & the Discriminant& the Discriminant
22
The Quadratic FormulaThe Quadratic Formula
2
2
0 :
4
2
The solutions of
ax bx c are
b b acx
a
33
ExamplesExamples21. 3 8 35x x
23 8 35 0x x 3; 8; 35a b c
28 8 4(3)( 35)
2(3)x
Have to write in standard form first!
2 4
2
b b acx
a
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28 8 4(3)( 35)
2(3)x
8 64 420
6x
8 484
6x
8 22
6x
55
8 22 8 22 or
6 6x x
8 22
6x
14 30 or
6 6x x
7 or 5
3x x
66
ExamplesExamples22. 12 5 2 13x x
22 12 18 0x x 2; 12; 18a b c
212 ( 12) 4(2)(18)
2(2)x
2 4
2
b b acx
a
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12 144 144
4x
12 0
4x
12
4x
212 ( 12) 4(2)(18)
2(2)x
3x
88
ExamplesExamples23. -2 2 3x x
22 2 3 0x x 2; 2; 3a b c
22 ( 2) 4(2)(3)
2(2)x
2 4
2
b b acx
a
99
2 4 24
4x
2 20
4x
2 2 5
4
ix
22 ( 2) 4(2)(3)
2(2)x
1010
2 2 5
4 4
ix
2 2 5
4
ix
1 5
2 2
ix
Split them up!!!
Sometimes one will simplify and the other won’t!
1111
HomeworkHomework
p.295 p.295 #17-29 first column#17-29 first column
#33-43 odds #33-43 odds
ADD YOUR HOMEWORK FOR ADD YOUR HOMEWORK FOR TODAY TO YESTERDAY’S!!!TODAY TO YESTERDAY’S!!!
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Algebra 2: Section 5.6Algebra 2: Section 5.6
The Quadratic Formula & The Quadratic Formula & the Discriminantthe Discriminant
(Day 2)(Day 2)
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The DiscriminantThe Discriminant
The expression The expression underunder the radical the radical in the quadratic formulain the quadratic formula
2 4b ac
2 4
2
b b acx
a
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The DiscriminantThe Discriminant
If discriminant is If discriminant is positivepositive–Two real solutionsTwo real solutions
If discriminant is If discriminant is zerozero–One real solutionOne real solution
If discriminant is If discriminant is negativenegative–Two imaginary solutionsTwo imaginary solutions
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ExamplesExamples
Use the discriminant to determine the number Use the discriminant to determine the number and type of solutions of the equation.and type of solutions of the equation.
21. 9 6 1 0x x 9; 6; 1a b c
26 4(9)(1)
2 4b ac
36 36 One real solution0
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ExamplesExamples22. 9 6 4 0x x 9; 6; 4a b c
26 4(9)( 4)
2 4b ac
36 144
Two real solutions
180
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ExamplesExamples23. 9 6 5 0x x 9; 6; 5a b c
26 4(9)(5)
2 4b ac
36 180
Two imaginary solutions
144
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HomeworkHomework
p.296 p.296 #46-67 all#46-67 all
Look at 46 – 55……Look at 46 – 55……