Question

a) x2 - 2x + 1 = 0 k) x2 – x – 1 = 0 b) x2 + 4x = 0 l) 5x2 +x + 4 = 0 c) x2 - 3 = 0 m) -2x2 – 8x – 1 = 0 d) x2 - 3x + 2 = 0 n) -6x2 +3x = 0 e) 4x2 - x = 0 o) -5x +x2 – 1 = 0 f) 9x2 - 1 = 0 g) 2x2 + 5x - 6 = 0 h) x2 - 5x + 1 = 0 i) -1 +x2 =0 j) 8x2 = 0

Answer 1

Explicação passo-a-passo:

a)

x² - 2x + 1 = 0

(x - 1)² = 0

x - 1 = 0

x' = x" = 1

S = {1}

b)

x² + 4x = 0

x.(x + 4) = 0

• x' = 0

• x + 4 = 0

x" = -4

S = {-4, 0}

c)

x² - 3 = 0

x² = 3

x = ±√3

• x' = √3

• x" = -√3

S = {-√3, √3}

d)

x² - 3x + 2 = 0

x² - x - 2x + 2 = 0

x.(x - 1) - 2.(x - 1) = 0

(x - 1).(x - 2) = 0

• x - 1 = 0

x' = 1

• x - 2 = 0

x" = 2

S = {1, 2}

e)

4x² - x = 0

x.(4x - 1) = 0

• x' = 0

• 4x - 1 = 0

4x = 1

x" = 1/4

S = {0, 1/4}

f)

9x² - 1 = 0

9x² = 1

x² = 1/9

x = ±√1/9

• x' = 1/3

• x" = -1/3

S = {-1/3, 1/3}

g)

2x² + 5x - 6 = 0

Δ = 5² - 4.2.(-6)

Δ = 25 + 48

Δ = 73

x = (-5 ± √73)/2.2

x = (-5 ± √73)/4

• x' = (-5 + √73)/4

• x" = (-5 - √73)/4

S = {(-5 - √73)/4, (-5 + √73)/4}

h)

x² - 5x + 1 = 0

Δ = (-5)² - 4.1.1

Δ = 25 - 4

Δ = 21

x = (5 ± √21)/4

• x' = (5 + √21)/4

• x" = (5 - √21)/4

S = {(5 - √21)/4, (5 + √21)/4}

i)

-1 + x² = 0

x² = 1

x = ±√1

• x' = 1

• x" = -1

S = {-1, 1}

j)

8x² = 0

x² = 0/8

x² = 0

x =±√0

• x' = x" = 0

S = {0}

k)

x² - x - 1 = 0

Δ = (-1)² - 4.1.(-1)

Δ = 1 + 4

Δ = 5

x = (1 ± √5)/2

• x' = (1 + √5)/2

• x" = (1 - √5)/2

S = {(1 - √5)/2, (1 + √5)/2}

l)

5x² + x + 4 = 0

Δ = 1² - 4.5.4

Δ = 1 - 80

Δ = -79

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S = { }

m)

-2x² - 8x - 1 = 0

Δ = (-8)² - 4.(-2).(-1)

Δ = 64 - 8

Δ = 56

x = (8 ± √56)/2.(-2)

x = (8 ± 2√14)/(-4)

• x' = (8 + 2√14)/(-4)

x' = (-4 - √14)/2

• x" = (8 - 2√14)/(-4)

x" = (-4 + √14)/2

S = {(-4 - √14)/2, (-4 + √14)/2}

n)

-6x² + 3x = 0

3x.(-2x + 1) = 0

• 3x = 0

x = 0/3

x' = 0

• -2x + 1 = 0

2x = 1

x" = 1/2

S = {0, 1/2}

o)

-5x + x² - 1 = 0

x² - 5x - 1 = 0

Δ = (-5)² - 4.1.(-1)

Δ = 25 + 4

Δ = 29

x = (5 ± √29)/2

• x' = (5 + √29)/2

• x" = (5 - √29)/2

S = {(5 - √29)/2, (5 + √29)/2}