Question

Oi gente estou com dificuldade nas equações de 2°grau completa, alguém poderia me ajudar?

Answer 1

Resposta:

a) S = {2, 5}

b) S = {3, 3}

c) S = {}

d) S = {}

e) S = {-2, 3}

f) S = {0, 5}

g) S = {3, -1/2}

h) S = {0, 5}

i) S = {-3, 4}

j) S = {8, 8}

Explicação passo-a-passo:

a) x² - 7x + 10 = 0

a = 1

b = -7

c = 10

∆ = (-7)² -4.1.10

∆ = 49 - 40

∆ = 9

x = -(-7) ± √9/2.1

x = 7 ± 3/2

x' = 7 + 3/2

x' = 10/2

x' = 5

x" = 7 - 3/2

x" = 4/2

x" = 2

S = {2, 5}

b) x² - 6x + 9 = 0

a = 1

b = -6

c = 9

∆ = (-6)² - 4.1.9

∆ = 36 - 36

∆ = 0

x = -(-6) ± √0/2.1

x = 6 ± 0/2

x' = 6 + 0/2

x' = 6/2

x' = 3

x" = 6 - 0/2

x" = 6/2

x" = 3

S = {3, 3}

c) 2x² + x + 5 = 0

a = 2

b = 1

c = 5

∆ = 1² - 4.2.5

∆ = 1 - 40

∆ = -39

S = {}

d) 7x² + x + 1 = 0

a = 7

b = 1

c = 1

∆ = 1² - 4.7.1

∆ = 1 - 28

∆ = -27

S = {}

e) x² - x - 1 = 0

a = 1

b = -1

c = -1

∆ = (-1)² - 4.1.(-1)

∆ = 1 + 4

∆ = 5

x = -(-1) ± √5/2.1

x = 1 ± 5/2

x' = 1 + 5/2

x' = 6/2

x' = 3

x" = 1 - 5/2

x" = -4/2

x" = -2

S = {-2, 3}

f) x² - 5x = 0

x (x - 5) = 0

x = 5

S = {0, 5}

g) 2x² - 5x - 3 = 0

a = 2

b = -5

c = -3

∆ = (-5)² - 4.2.(-3)

∆ = 25 + 24

∆ = 49

x = -(-5) ± √49/2.2

x = 5 ± 7/4

x' = 5 + 7/4

x' = 12/4

x' = 3

x" = 5 - 7/4

x" = -2/4

x" = -1/2

S = {3, -1/2}

h) x² - 5x = 0

x (x - 5) = 0

x = 5

S = {0, 5}

i) -x² + x + 12 = 0

a = -1

b = 1

c = 12

∆ = 1² - 4.(-1).12

∆ = 1 + 48

∆ = 49

x = -1 ± √49/2.(-1)

x = -1 ± 7/-2

x' = -1 + 7/-2

x' = 6/-2

x' = -3

x" = -1 - 7/-2

x" = -8/-2

x" = 4

S = {-3, 4}

j) -x² + 16x - 64 = 0

a = -1

b = 16

c = -64

∆ = 16² - 4.(-1).(-64)

∆ = 256 - 256

∆ = 0

x = -16 ± √0/2.(-1)

x = -16 ± 0/-2

x' = -16 + 0/-2

x' = -16/-2

x' = 8

x" = -16 - 0/-2

x" = -16/-2

x" = 8

S = {8, 8}