Question

a)X² + 7x + 12= 0
b)X² + 5x + 4= 0
c)X² - x + 30= 0
d)X² - 6x + 9= 0
e)X² + 3x 28= 0
f)3x² - 4x + 2= 0
g)x² - 4x - 5= 0

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Answer 1

Resposta:

a) X² + 7x + 12= 0

x = - b ± √b² - 4.a.c / 2.a

x = - 7 ± √7² - 4.1.12 / 2.1

x = - 7 ± √49 - 48 / 2        

x = - 7 ± √1 / 2

x = - 7 ± 1 / 2

x' = - 7 + 1 / 2 =  - 6 / 2 = - 3

x" = - 7 - 1 / 2 = - 8 / 2 = - 4

S= {(- 3, - 4)}

b) X² + 5x + 4= 0

x = - 5 ± √5² - 4.1.4 / 2.1

x = - 5 ± √25 - 16 / 2        

x = - 5 ± √9 / 2

x = - 5 ± 3 / 2

x' = - 5 + 3/ 2 =  - 2 / 2 = - 1

x" = - 5 - 3 / 2 = - 8 / 2 = - 4

S= {(- 1, - 4)}

c) X² - x + 30= 0

x = - (- 1) ± √(-1)² - 4.1.30 / 2.1

x = 1 ± √1 - 120 / 2        

x = 1 ± √-119 / 2

x = 1 / 2

x' = x" = 1 / 2

S = {(1/2)}

d) X² - 6x + 9= 0

x = - (- 6) ± √(-6)² - 4.1.9 / 2.1

x = 6 ± √(-6) - 4. 1 . 9 / 2        

x = 6 ± √36 - 36 / 2

x = 6 ± √0/ 2

x' = x" = 6 / 2 = 3

S = {(3)}

e) X² + 3x + 28= 0

x = - 3 ± √(3)² - 4.1.28 / 2.1

x = - 3 ± √9 + 112 / 2        

x = - 3 ± √121 / 2

x = - 3 ± 11 / 2

x' = - 3 + 11 / 2 = 8 / 2 = 4

x" = - 3 - 11 / 2 = - 14 / 2 = - 7

S = {(4, - 7)}

f) 3x² - 4x + 2= 0

x = - (- 4) ± √(-4)² - 4.3.2 / 2.3

x = 4 ± √16 - 16 / 6        

x = 4 ± √0/ 6

x = 4  / 2

x' = x" = 4 / 2 = 2

S = {(2)}

g)x² - 4x - 5= 0

x = - (- 4) ± √(-4)² - 4.1.- 5 / 2.1

x = 4 ± √16 + 20 / 2        

x = 4 ± √36/ 2

x = 4 ± 6 / 2

x' = 4 + 6 / 2 = 10 / 2 = 5

x" = 4 - 6 / 2 = - 2 / 2 = - 1

S = {(5, - 1)}

Explicação passo a passo: