Question

Resolva as equações do 2º grau
a) x² + x-6=0
b) x²+4x+4=0
c) x²+5x-6=0
d) x²+x-2=0
alguém me ajuda por favor​

Answer 1

a) x² + x - 6 = 0

a = 1

b = 1

c = - 6

∆ = b² - 4 . a . c

∆ = 1² - 4 . 1 . (-6)

∆ = 1 + 24

∆ = 25

x = - b ± √∆

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2a

x' = - 1 + 5

--------

2 . 1

x' = 4

---

2

x' = 2

x" = - 1 - 5

--------

2 . 1

x" = - 6

----

2

x" = - 3

S = {2 , -3}

b) x² + 4x + 4 = 0

a = 1

b = 4

c = 4

∆ = b² - 4 . a . c

∆ = 4² - 4 . 1 . 4

∆ = 16 - 16

∆ = 0 (as raízes são iguais)

x = - b ± √∆

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

2a

x = - 4 - 0

---------

2 . 1

x = - 4

---

2

x = - 2

S = {-2}

c) x² + 5x - 6 = 0

a = 1

b = 5

c = - 6

∆ = b² - 4 . a . c

∆ = 5² - 4 . 1 . (-6)

∆ = 25 + 24

∆ = 49

x = - b ± √∆

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

2a

x' = - 5 + 7

---------

2 . 1

x' = 2

---

2

x' = 1

x" = - 5 - 7

---------

2 . 1

x" = - 12

---

2

x" = - 6

S = {1 , -6}

d) x² + x - 2 = 0

a = 1

b = 1

c = - 2

∆ = b² - 4 . a . c

∆ = 1² - 4 . 1 . (-2)

∆ = 1 + 8

∆ = 9

x = - b ± √∆

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

2a

x' = - 1 + 3

---------

2 . 1

x' = 2

---

2

x' = 1

x" = - 1 - 3

--------

2 . 1

x" = - 4

---

2

x" = - 2

S = {1 , -2}