Question

Atividade de Matemática
1º) Resolva as equações do 2º grau a seguir.
a) X2 + 5x + 6 = 0
b) X2 - 3x + 2 = 0
c) X? -5x + 6 = 0
d) x2 + 3x - 4 = 0
e) X - 2x - 8 = 0
f) 3x2 + 4x - 4 = 0​

Answer 1

  a) x² + 5x + 6 = 0

a = 1

b = 5

c = 6

∆ = b² - 4 . a . c

∆ = 5² - 4 . 1 . 6

∆ = 25 - 24

∆ = 1

x = -b ± √∆ / 2 . a

x = -5 ± √1 / 2 . 1

x = -5 ± 1 / 2

x¹ = -5 + 1 / 2

x¹ = -4 / 2

x¹ = -2

x² = -5 - 1 / 2

x² = -6 / 2

x² = -3

S = {-2 ; -3}

  b) x² -3x + 2 = 0

a = 1

b = -3

c = 2

∆ = b² - 4 . a . c

∆ = (-3)² - 4 . 1 . 2

∆ = 9 - 8

∆ = 1

x = -b ± √∆ / 2 . a

x = -(-3) ± √1 / 2 . 1

x = 3 ± 1 / 2

x¹ = 3 + 1 / 2

x¹ = 4 / 2

x¹ = 2

x² = 3 - 1 / 2

x² = 2 / 2

x² = 1

S = {2 ; 1}

  c) x² - 5x + 6 = 0

a = 1

b = -5

c = 6

∆ = b² - 4 . a . c

∆ = (-5)² - 4 . 1 . 6

∆ = 25 - 24

∆ = 1

x = -b ± √∆ / 2 . a

x = -(-5) ± √1 / 2 . 1

x = 5 ± 1 / 2

x¹ = 5 + 1 / 2

x¹ = 6 / 2

x¹ = 3

x² = 5 - 1 / 2

x² = 4 / 2

x² = 2

S = {3 ; 2}

  d) x² + 3x - 4 = 0

a = 1

b = 3

c = -4

∆ = b² - 4 . a . c

∆ = 3² - 4 . 1 . (-4)

∆ = 9 + 16

∆ = 25

x = -b ± √∆ / 2 . a

x = -3 ± √25 / 2 . 1

x = -3 ± 5 / 2

x¹ = -3 + 5 / 2

x¹ = 2 / 2

x¹ = 1

x² = -3 - 5 / 2

x² = -8 / 2

x² = -4

S = {1 ; -4}

  e) x² - 2x - 8 = 0

a = 1

b = -2

c = -8

∆ = b² - 4 . a . c

∆ = (-2)² - 4 . 1 . (-8)

∆ = 4 + 32

∆ = 36

x = -b ± √∆ / 2 . a

x = -(-2) ± √36 / 2 . 1

x = 2 ± 6 / 2

x¹ = 2 + 6 / 2

x¹ = 8 / 2

x¹ = 4

x² = 2 - 6 / 2

x² = -4 / 2

x² = -2

S = {4 ; -2}

  f) 3x² + 4x - 4 = 0

a = 3

b = 4

c = -4

∆ = b² - 4 . a . c

∆ = 4² - 4 . 3 . (-4)

∆ = 16 + 48

∆ = 64

x = -b ± √∆ / 2 . a

x = -4 ± √64 / 2 . 3

x = -4 ± 8 / 6

x¹ = -4 + 8 / 6

x¹ = 4 / 6

x² = -4 - 8 / 6

x² = -12 / 6

x² = -2

S = {4/6 ; -2}

Respostas sublinhadas!

Boa Sorte! :3