Question

2- Resolva as seguintes equações do 2º grau: a) x2 - x - 20 = 0
b) x2 - 3x -4 = 0
c) x2 - 8x + 7 = 0
d) x ( x + 3) – 40
e) 7x² + x + 2 = 0
f) (x - 5)² = 1​

Answer 1

Explicação passo-a-passo:

x2 - x - 20 = 0

a= 1; b = -1; c = -20

D = -1² - 4 . 1 . (-20)

D = 1 + 80

D = 81

x' = -(-1) + 9

2 . 1

x' = 1 + 9

2

x' = 10

2

x' = 5

x" = -(-1) - 9

2 . 1

x" = 1 - 9

2

x'' = -8

2

x'' = -4

b) x2 - 3x -4 = 0

a= 1; b = -3; c = -4

D = -3² - 4 . 1 . (-4)

D = 9 + 16

D = 25

x' = -(-3) + 5

2 . 1

x' = 3 + 5

2

x' = 8

2

x' = 4

x" = -(-3) - 5

2 . 1

x" = 3 - 5

2

x'' = -2

2

x'' = -1

c) x2 - 8x + 7 = 0

a= 1; b = -8; c = 7

D = -8² - 4 . 1 . 7

D = 64 - 28

D = 36

x' = -(-8) + 6

2 . 1

x' = 8 + 6

2

x' = 14

2

x' = 7

x" = -(-8) - 6

2 . 1

x" = 8 - 6

2

x'' = 2

2

x'' = 1

d) x ( x + 3) – 40

x² + 3x - 40 = 0

a= 1; b = 3; c = -40

D = 3² - 4 . 1 . (-40)

D = 9 + 160

D = 169

x' = -3 + 13

2 . 1

x' = -3 + 13

2

x' = 10

2

x' = 5

x" = -3 - 13

2 . 1

x" = -3 - 13

2

x'' = -16

2

x'' = -8

e) 7x² + x + 2 = 0

a= 7; b = 1; c = 2

D = 1² - 4 . 7 . 2

D = 1 - 56

D = -55

f) (x - 5)² = 1

x² - 10x + 25 - 1 = 0

x² - 10x + 24 = 0

a= 1; b = -10; c = 24

D = -10² - 4 . 1 . 24

D = 100 - 96

D = 4

x' = -(-10) + 2

2 . 1

x' = 10 + 2

2

x' = 12

2

x' = 6

x" = -(-10) - 2

2 . 1

x" = 10 - 2

2

x'' = 8

2

x'' = 4