Question

Achar as raízes das equações: 2) x2 - x - 20 = 0 b) x2 - 3X -4 = 0 C) x2 - 8x + 7 = 0​

Answer 1

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

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2

x' = - 8

---

2

x' = - 4

x" = - (-1) + 9

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2 . 1

x" = 1 + 9

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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 ± √∆

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2a

x' = - (-3) - 5

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2 . 1

x' = 3 - 5

--------

2

x' = - 2

---

2

x' = - 1

x" = - (-3) + 5

------------

2 . 1

x" = 3 + 5

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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

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2

x' = 2

---

2

x' = 1

x" = - (-8) + 6

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2 . 1

x" = 8 + 6

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2

x" = 14

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2

x" = 7

S = {1 , 7}