Achar as raízes das equações: 2) x2 - x - 20 = 0 b) x2 - 3X -4 = 0 C) x2 - 8x + 7 = 0
Soluções para a tarefa
a) x² - x - 20 = 0
a = 1
b = - 1
c = - 20
∆ = b² - 4 . a . c
∆ = (-1)² - 4 . 1 . (-20)
∆ = 1 + 80
∆ = 81
x = - b ± √∆
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2a
x' = - (-1) - 9
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2 . 1
x' = 1 - 9
-------
2
x' = - 8
---
2
x' = - 4
x" = - (-1) + 9
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2 . 1
x" = 1 + 9
-------
2
x" = 10
---
2
x" = 5
S = {-4 , 5}
b) x² - 3x - 4 = 0
a = 1
b = - 3
c = - 4
∆ = b² - 4 . a . c
∆ = (-3)² - 4 . 1 . (-4)
∆ = 9 + 16
∆ = 25
x = - b ± √∆
------------
2a
x' = - (-3) - 5
-----------
2 . 1
x' = 3 - 5
--------
2
x' = - 2
---
2
x' = - 1
x" = - (-3) + 5
------------
2 . 1
x" = 3 + 5
-------
2
x" = 8
---
2
x" = 4
S = {-1 , 4}
c) x² - 8x + 7 = 0
a = 1
b = - 8
c = 7
∆ = b² - 4 . a . c
∆ = (-8)² - 4 . 1. 7
∆ = 64 - 28
∆ = 36
x = - b ± √∆
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2a
x' = - (-8) - 6
-----------
2 . 1
x' = 8 - 6
-------
2
x' = 2
---
2
x' = 1
x" = - (-8) + 6
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2 . 1
x" = 8 + 6
-------
2
x" = 14
---
2
x" = 7
S = {1 , 7}