Respostas
3) 6x² + x - 1 = 0
∆ = b² - 4 . a . c
∆ = 1² - 4 . 6 . (-1)
∆ = 1 + 24
∆ = 25
x = - b ± ✓∆
------------
2a
x' = - 1 - 5
--------
2 . 6
x' = - 6 (÷6)
---
12 (÷6)
x' = - 1
---
2
x" = - 1 + 5
---------
2 . 6
x" = 4 (÷4)
---
12 (÷4)
x" = 1
---
3
S = {-1/2 , 1/3}
4) 3x² - 7x + 2 = 0
∆ = b² - 4 . a . c
∆ = (-7)² - 4 . 3 . 2
∆ = 49 - 24
∆ = 25
x = - b ± √∆
------------
2a
x' = -(-7) - 5
-----------
2 . 3
x' = 7 - 5
-------
6
x' = 2 (÷2)
---
6 (÷2)
x' = 1
---
3
x" = -(-7) + 5
-----------
2 . 3
x" = 7 + 5
--------
6
x" = 12
----
6
x" = 2
S = {1/3 , 2}
5) 2x² - 7x - 15 = 0
∆ = b² - 4 . a . c
∆ = (-7)² - 4 . 2 . (-15)
∆ = 49 + 120
∆ = 169
x = - b ± √∆
------------
2a
x' = -(-7) - 13
-------------
2 . 2
x' = 7 - 13
--------
4
x' = - 6 (÷2)
---
4 (÷2)
x' = - 3
---
2
x" = -(-7) + 13
------------
2 . 2
x" = 7 + 13
---------
4
x" = 20
----
4
x" = 5
S = {-3/2 , 5}
6) 4x² - 12x + 9 = 0
∆ = b² - 4 . a . c
∆ = (-12)² - 4 . 4 . 9
∆ = 144 - 144
∆ = 0
x = - b ± √∆
------------
2a
x = -(-12) - 0
------------
2 . 4
x = 12 - 0
-------
8
x = 12 (÷4)
---
8 (÷4)
x = 3
---
2
S = {3/2}
7) 2x² - 8x + 8 = 0
∆ = b² - 4 . a . c
∆ = (-8)² - 4 . 2 . 8
∆ = 64 - 64
∆ = 0
x = - b ± √∆
------------
2a
x' = -(-8) - 0
-----------
2 . 2
x' = 8 - 0
-------
4
x' = 8
---
4
x' = 2
S = {2}