Question

1=Resolva
$6x2 + x - 1 = 0$
$x2 + 7x + 10 = 0$
$x2 - 2x - 15 = 0$
$2 x 2 + 5x - 3 = 0$

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Answer 1

6x² + x - 1 = 0

a = 6, b = 1, c = - 1

Δ = b² - 4ac

Δ = 1² - 4 · 6 · (- 1)

Δ = 1 + 24

Δ = 25

x = - b ± √Δ / 2a

x = - 1 ± √25 / 2 · 6

x = - 1 ± 5 / 12

x' = - 1 + 5 / 12 = 4 / 12 = 1/3

x'' = - 1 - 5 / 12 = - 6 / 12 = - 1/2

S = {- ¹/₂, ¹/₃}

x² + 7x + 10 = 0

a = 1, b = 7, c = 10

Δ = b² - 4ac

Δ = 7² - 4 · 1 · 10

Δ = 49 - 40

Δ = 9

x = - b ± √Δ / 2a

x = - 7 ± √9 / 2 · 1

x = - 7 ± 3 / 2

x' = - 7 + 3 / 2 = - 4 / 2 = - 2

x'' = - 7 - 3 / 2 = - 10 / 2 = - 5

S = {- 5, - 2}

x² - 2x - 15 = 0

a = 1, b = - 2, c = - 15

Δ = b² - 4ac

Δ = (- 2)² - 4 · 1 · (- 15)

Δ = 4 + 60

Δ = 64

x = - b ± √Δ / 2a

x = - (- 2) ± √64 / 2 · 1

x = 2 ± 8 / 2

x' = 2 + 8 / 2 = 10 / 2 = 5

x'' = 2 - 8 / 2 = - 6 / 2 = - 3

S = {- 3, 5}

2x² + 5x - 3 = 0

a = 2, b = 5, c = - 3

Δ = b² - 4ac

Δ = 5² - 4 · 2 · (- 3)

Δ = 25 + 24

Δ = 49

x = - b ± √Δ / 2a

x = - 5 ± √49 / 2 · 2

x = - 5 ± 7 / 4

x' = - 5 + 7 / 4 = 2 / 4 = 1/2

x'' = - 1 - 7 / 4 = - 12 / 4 = - 3

S = {- 3, ¹/₂}