Question

1-Resolva as seguinte equações do 2º grau:

A: -5x²-7x+6=0

B: -x²-4x-2=0

C: x²-9x+8=0

D: x²-x-12=0

E: x² -11x+18=0

F: x²-4x-12=0

Answer 1

a)
- 5x² - 7x + 6 = 0
a = - 5; b = - 7; c = 6

Δ = b² - 4ac
Δ = (-7)² - 4.(- 5).6
Δ = 49 + 20.6
Δ = 49 + 120
Δ = 169

x =  7 + 13 = 20/-20 = - 1
        - 20

x =  7 - 13 =  - 6   (: - 2)  =  3
        - 20      - 20  (:-  2)     10
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b)
- x² - 4x - 2 = 0
a = -1; b = - 4; c = - 2

Δ = b² - 4ac
Δ = (-4)² - 4.(-1).(-2)
Δ = 16 + 4.(-2)
Δ = 16 - 8
Δ = 8
√Δ = √8
√Δ = √4.√2
√Δ = 2√2

x = - b +/- √Δ = - ( - 4) +/- √8
          2a                2.(-1)

x = 4 + 2√2 = - 2 - √2
        - 2

x = 4 - 2√2 = - 2 + √2
        - 2
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c)
x² - 9x + 8 = 0
a = 1; b = - 9; c = 8

Δ = b² - 4ac
Δ = (-9)² - 4.1.8
Δ = 81 - 32
Δ = 49

x = 9 + 7 = 16/2 = 8
        2

x = 9 - 7 = 2/2 = 1
        2
R.: x = 1 e x = 8
(((((((((((((((((((((((((((((((((((((((((((

d)
x² - x - 12 = 0

a = 1; b = - 1; c = - 12

Δ = b² - 4ac
Δ = (-1)² - 4.1.(-12)
Δ = 1 + 48
Δ = 49

x = 1 + 7 = 8/2 = 4
        2

x = 1 - 7 = - 6/2 = - 3
        2

R.: x = 4 e x = - 3
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e)
x² - 11x + 18 = 0
a = 1; b = - 11; c = 18

Δ = b² - 4ac
Δ = ( - 11)² - 4.1.18
Δ = 121 - 72
Δ = 49

x = 11 + 7 = 18/2 = 9
         2

x = 11 - 7 = 4/2 = 2
         2

R.: x = 9 e x = 2
)))))))))))))))))))))))))))))))))))))
f)
x² - 4x - 12 = 0
a = 1; b = - 4; c = - 12

Δ = b² - 4ac
Δ = (-4)² - 4.1.(-12)
Δ = 16 + 48
Δ = 64

x = 4 + 8 = 12/2 = 6
        2

x = 4 - 8 = - 4/2 = - 2
         2

R.: x = 6 e x = - 2