Question

determine as raizes das equação

a) 3x² -6x -72=0

b)-2(x+1)(x-3)=0

Answer 1

Resoluções

3x² - 6x - 72 = 0 (÷3)
x² - 2x - 24 = 0 --> a = 1 b = - 2 c = - 24

x = - b ± √b² - 4.a.c / 2.a
x = -(-2) ± √(-2)² - 4. 1. -24 / 2 . 1
x = 2 ± √4 + 96 / 2
x = 2 ± √100 / 2
x = 2 ± 10 / 2

x' = 2 + 10 / 2 = 12 / 2 = 6
x " = 2 - 10 / 2 = - 8 / 2 = - 4

S = {6 ; - 4}

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- 2.(x + 1)(x - 3) = 0
- 2.(x² - 3x + x - 3) = 0
- 2.(x² - 2x - 3) = 0
- 2x + 4x + 6 = 0 (÷2)
- x² + 2x + 3 = 0 a= -1 b= 2 c= 3

x = - b ± √b² - 4. a. c / 2. a
x = - 2 ± √2² - 4. - 1. 3 / 2. - 1
x = - 2 ± √ 4 + 12 / - 2
x = - 2 ± √16 / - 2
x = - 2 ± 4 / - 2

x' = - 2 + 4 / - 2 = 2 / - 2 = - 1
x" = - 2 - 4 / - 2 = - 6 / - 2 = 3

S = { - 1 ; 3 }