Question

1) Resolva as equações do 2º grau:
a) x2 - 5x + 6 = 0
b) x2 - 8x + 12 = 0
C) -x2 + x + 12 = 0
d) 4x2 - x + 1 = x + 3x2
e) 3x2 + 5x = -x – 9 + 2x2
f) 4+ x (x - 4) = X
g) x2 - 18x + 45 = 0
h) (x - 5)2 = 1

Answer 1

a) x² - 5x + 6 = 0

∆ = b² - 4 . a . c

∆ = (-5)² - 4 . 1 . 6

∆ = 25 - 24

∆ = 1

x = - b ± √∆

-----------

2a

x' = -(-5) - 1

----------

2 . 1

x' = 5 - 1

-------

2

x' = 4

---

2

x' = 2

x" = -(-5) + 1

-----------

2 . 1

x" = 5 + 1

-------

2

x" = 6

---

2

x" = 3

b) x² - 8x + 12 = 0

∆ = b² - 4 . a . c

∆ = (-8)² - 4 . 1 . 12

∆ = 64 - 48

∆ = 16

x = - b ± √∆

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

2a

x' = -(-8) - 4

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

2 . 1

x' = 8 - 4

-------

2

x' = 4

---

2

x' = 2

x" = -(-8) + 4

-----------

2 . 1

x" = 8 + 4

--------

2

x" = 12

----

2

x" = 6

c) - x² + x + 12 = 0

∆ = b² - 4 . a . c

∆ = 1² - 4 . (-1) . 12

∆ = 1 + 48

∆ = 49

x = - b ± √∆

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

2a

x' = - 1 - 7

--------

2 . (-1)

x' = - 8

-----

- 2

x' = 4

x" = - 1 + 7

---------

2 . (-1)

x" = 6

----

- 2

x" = - 3

d) 4x² - x + 1 = x + 3x²

4x² - 3x² - x - x + 1

x² - 2x + 1 = 0

∆ = b² - 4 . a . c

∆ = (-2)² - 4 . 1 . 1

∆ = 4 - 4

∆ = 0

x = - b ± √∆

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

2a

x' = -(-2) - 0

-----------

2 . 1

x' = 2 - 0

-------

2

x' = 2

---

2

x' = 1

x" = -(-2) + 0

-----------

2 . 1

x" = 2 + 0

-------

2

x" = 2

---

2

x" = 1

e) 3x² + 5x = - x - 9 + 2x²

3x² - 2x² + 5x + x + 9

x² + 6x + 9 = 0

∆ = b² - 4 . a . c

∆ = 6² - 4 . 1 . 9

∆ = 36 - 36

∆ = 0

x = - b ± √∆

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

2a

x' = - 36 - 0

-----------

2 . 1

x' = - 36

-----

2

x' = - 18

x" = - 36 + 0

-----------

2 . 1

x" = - 36

-------

2

x" = - 18

f) 4 + x (x - 4) = x

4 + x² - 4x = x

4 + x² - 4x - x

x² - 5x + 4 = 0

∆ = b² - 4 . a . c

∆ = (-5)² - 4 . 1 . 4

∆ = 25 - 16

∆ = 9

x = - b ± √∆

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

2a

x' = -(-5) - 3

-----------

2 . 1

x' = 5 - 3

-------

2

x' = 2

---

2

x' = 1

x" = -(-5) + 3

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

2 . 1

x" = 5 + 3

-------

2

x" = 8

---

2

x" = 4

g) x² - 18x + 45 = 0

∆ = b² - 4 . a . c

∆ = (-18)² - 4 . 1 . 45

∆ = 324 - 180

∆ = 144

x = - b ± √∆

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

2a

x' = -(-18) - 12

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

2 . 1

x' = 18 - 12

---------

2

x' = 6

---

2

x' = 3

x" = -(-18) + 12

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

2 . 1

x" = 18 + 12

----------

2

x" = 30

----

2

x" = 15

h) (x - 5)² = 1

x² - 2 . x . 5 + 5² = 1

x² - 10x + 25 = 1

x² - 10x + 25 - 1

x² - 10x + 24 = 0

∆ = b² - 4 . a . c

∆ = (-10)² - 4 . 1 . 24

∆ = 100 - 96

∆ = 4

x = - b ± √∆

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

2a

x' = -(-10) - 2

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

2 . 1

x' = 10 - 2

--------

2

x' = 8

---

2

x' = 4

x" = -(-10) + 2

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

2 . 1

x" = 10 + 2

--------

2

x" = 12

---

2

x" = 6