Question

Indique os zeros das seguintes equações:

a) x2 + 2x = 0

b) x2 – 4 = 0


c) x2 – 7x + 10 = 0

d) 2x2 – 3x + 4 = 0


e) x2 + 2x + 1 = 0​

Answer 1

Explicação passo-a-passo:

a×2+2×=4

b×2-4=2

c×2-7×+10=55

d2×2-3×+4=5

e2×+2×2+1=9

Answer 2

Resposta:

a) x'= 0

x" = - 4

b) x' = 2

x" = -2

c) x' = 5

x" = 2

d) x'= 3 + √41 / 4

x" = 3 - √41 / 4

e) x'= -1

x" = -2

Explicação passo-a-passo:

a) x² + 2x = 0

Δ = b² - 4.a.c

Δ = 2² - 4 × 1 × 0

Δ = 4 - 0

Δ = 4

x = -b ± √Δ / 2.a

x = - 2 ± √4 / 2 × 1

x = - 2 ± 2 / 2

x' = - 2 + 2 / 2

x' = 0

x" = - 2 - 6 / 2

x" = - 8 / 2 = - 4

b) x² – 4 = 0

Δ = b² - 4.a.c

Δ = 0² - 4 × 1 × (-4)

Δ = 0 + 16

Δ = 16

x = -b ± √Δ / 2.a

x = - 0 ± √16 / 2 × 1

x = 0 ± 4 / 2

x' = 0 + 4 / 2

x' = 4 / 2 = 2

x" = 0 - 4 / 2

x" = - 4 / 2 = -2

c) x² – 7x + 10 = 0

Δ = b² - 4.a.c

Δ = (-7)² - 4 × 1 × 10

Δ = 49 - 40

Δ = 9

x = -b ± √Δ / 2.a

x = - (-7) ± √9 / 2 × 1

x = 7 ± 3 / 2

x' = 7 + 3 / 2

x' = 10 / 2 = 5

x" = 7 - 3 / 2

x" = 4 / 2 = 2

d) 2x² – 3x + 4 = 0

Δ = b² - 4.a.c

Δ = (-3)² - 4 × 2 × 4

Δ = 9 + 32

Δ = 41

x = -b ± √Δ / 2.a

x = - (-3) ± √41 / 2 × 2

x = 3 ± √41 / 4

x' = 3 + √41 / 4

x" = 3 - √41 / 4

e) x² + 2x + 1 = 0​

Δ = b² - 4.a.c

Δ = 2² - 4 × 1 × 1

Δ = 4 - 4

Δ = 0

x = -b ± √Δ / 2.a

x = - 2 ± √0 / 2 × 1

x = - 2 ± 0 / 2

x' = - 2 + 0 / 2

x' = - 2 / 2 = -1

x" = - 2 - 2 / 2

x" = -4 / 2 = -2