Question

Determine os zeros das funções:
a)y=x-6x+8
b)y=x-6x+9
c)y=3+2x
d)y=3x+2x
e)y=-x+x+2

Answer 1

a)
y = x² - 6x + 8
0 = x² - 6x + 8
x² - 6x + 8 = 0
a = 1; b = - 6; c = 8
Δ = b² - 4ac
Δ = (-6)² - 4.1.8
Δ = 36 - 32
Δ = 4

x = - b +/- √Δ    = - (-6) +/- √4
      --------------     ------------------
               2a                  2.1

x = 6 + 2
      ---------  = 8/2 = 4
          2

x = 6 - 2
      -------- = 4/2 = 2
          2

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b)
y = x² - 6x + 9 
0 = x² - 6x + 9
x² - 6x + 9 = 0
a = 1; b = - 6; c = 9
Δ = b² - 4ac
Δ = (-6)² - 4.1.9
Δ = 36 - 36
Δ = 0

x = - b +/- √Δ    =  - (-6) +/- √0
      --------------      ------------------
             2a                    2.1

x = 6/2 
x = 3

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c)
y = 3x² - 4x
0 = 3x² - 4x
3x² - 4x = 0
x.(3x - 4) = 0
x = 0

3x - 4 = 0
3x = 4
x = 4/3

R.: x = 0 e x = 4/3

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d)
y = 3x² + 2x
0 = 3x² + 2x
3x² + 2x = 0
x.(3x + 2) = 0
x = 0
3x + 2 = 0
3x = - 2
x = - 2/3

R.: x = 0 e x = - 2/3

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e)
y = - x² + x + 2
0 = - x² + x + 2
- x² + x + 2 = 0
a = - 1; b = 1; c = 2
Δ = b² - 4ac
Δ = 1² - 4.(-1).2
Δ = 1 + 4.2
Δ = 1 + 8
Δ = 9

x = - b +/- √Δ          - 1 +/- √9
      ---------------  = -----------------
               2a               2.(-1)

x = - 1 + 3
      ----------- = 2/(-2) = - 1
          - 2

x = - 1 - 3
       --------- = -4/(-2) = 2
          - 2

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