4. Resolva as seguintes equações de 2º grau:
a) 2x2 - 50 = 0
b) 5x2 - 15 = 0
c) 2x2 = 8x
d) 7x2 = - 14x
e) x2 + x - 7=5
f) 4x2 - x + 1 = x + 3x2
g) 3x2 + 5x = -x-9 + 2x2
Soluções para a tarefa
a) 2x² - 50 = 0
2x² = 0 + 50
2x² = 50
x² = 50
----
2
x² = 25
x = √25
x = ± 5
S = {-5 , +5}
b) 5x² - 15 = 0
5x² = 0 + 15
5x² = 15
x² = 15
---
5
x² = 3
x = √3
x = ± 1,73
S = {-1,73 , +1,73}
c) 2x² = 8x
2x² - 8x = 0
2x (x - 4) = 0
2x = 0
x = 0
---
2
x = 0
x - 4 = 0
x = 0 + 4
x = 4
S = {0 , 4}
d) 7x² = - 14x
7x² + 14x = 0
7x (x + 2) = 0
7x = 0
x = 0
---
7
x = 0
x + 2 = 0
x = 0 - 2
x = - 2
S = {0 , -2}
e) x² + x - 7 = 5
x² + x - 7 - 5
x² + x - 12 = 0
a = 1
b = 1
c = - 12
∆ = 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
S = {-4 , 3}
f) 4x² - x + 1 = x + 3x²
4x² - 3x² - x - x + 1
x² - 2x + 1 = 0
a = 1
b = - 2
c = 1
∆ = 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
S = {1}
g) 3x² + 5x = - x - 9 + 2x²
3x² - 2x² + 5x + x + 9
x² + 6x + 9 = 0
a = 1
b = 6
c = 9
∆ = b² - 4 . a . c
∆ = 6² - 4 . 1 . 9
∆ = 36 - 36
∆ = 0
x = - b ± √∆
------------
2a
x = - 6 - 0
---------
2 . 1
x = - 6
---
2
x = - 3
S = {-3}