Question

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Answer 1

1)

x² + x - 12 = 0

a= 1; b = 1; c = -12

Δ = b² - 4ac

Δ = 1² - 4 . 1 . (-12)

Δ = 1 + 48

Δ = 49

x = (-b ± √Δ)/2a

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 = {(-4, 3)}

Alternativa D.

2)

x² - 3x - 10 = 0

a= 1; b = -3; c = -10

Δ = b² - 4ac

Δ = (-3)² - 4 . 1 . (-10)

Δ = 9 + 40

Δ = 49

x = (-b ± √Δ)/2a

x = ( - (-3) ± √49)/2 . 1

x = (3 ± 7)/2

x' = (3 + 7)/2

x' = (10)/2

x' = 5

x'' = (3 - 7)/ 2

x = -4/ 2

x'' = -2

S = {(-2, 5)}

Alternativa A.

3)

-25x² - 10x - 1 = 0

a= -25; b = -10; c = -1

Δ = b² - 4ac

Δ = (-10)² - 4 . (-25) . (-1)

Δ = 100 - 100

Δ = 0

x = (-b ± √Δ)/2a

x = ( - (-10) ± √0)/2 . (-25)

x = (10 ± 0)/-50

x' = (10 + 0)/-50

x' = (10)/-50

x' = 1/-5

x'' = (10 - 0)/ -50

x = 10/ -50

x'' = -1/5

S = {(-1/5, -1/5)}

4)

2x² - 8x - 10 = 0

a= 2; b = -8; c = -10

Δ = b² - 4ac

Δ = (-8)² - 4 . 2 . (-10)

Δ = 64 + 80

Δ = 144

x = (-b ± √Δ)/2a

x = ( - (-8) ± √144)/2 . 2

x = (8 ± 12)/4

x' = (8 + 12)/4

x' = (20)/4

x' = 5

x'' = (8 - 12)/ 4

x = -4/ 4

x'' = -1

S = {(-1, 5)}

Alternativa C.

5)

3x² - 3 = 2x² + 2x

3x² - 2x² - 2x - 3 = 0

x² - 2x - 3 = 0

a= 1; b = -2; c = -3

Δ = b² - 4ac

Δ = (-2)² - 4 . 1 . (-3)

Δ = 4 + 12

Δ = 16

x = (-b ± √Δ)/2a

x = ( - (-2) ± √16)/2 . 1

x = (2 ± 4)/2

x' = (2 + 4)/2

x' = (6)/2

x' = 3

x'' = (2 - 4)/ 2

x = -2/ 2

x'' = -1

S = {(-1, 3)}

Alternativa C.

6)

2x- 4 = 0

2x = 4

x = 4/2

x = 2

ou

x + 3 = 0

x = - 3

Alternativa D.

7)

a = 1; b = -1; c = 6

x' + x" = -b/a

x' + x" = -(-1)/1

x' + x" = 1/1

x' + x" = 1

siga fundamentalmatematica no inst@gr@m

8)

a)

x(x + 9) + (x + 9) = 0

x² + 9x + x + 9 = 0

x² + 10x + 9 = 0

a= 1; b = 10; c = 9

Δ = b² - 4ac

Δ = 10² - 4 . 1 . 9

Δ = 100 - 36

Δ = 64

x = (-b ± √Δ)/2a

x = ( - 10 ± √64)/2 . 1

x = (-10 ± 8)/2

x' = (-10 + 8)/2

x' = (-2)/2

x' = -1

x'' = (-10 - 8)/ 2

x = -18/ 2

x'' = -9

S = {(-9, -1)}

b)

3x - 2 + 7x(3x - 2) = 0

3x - 2 + 21x² - 14x = 0

21x² - 11x - 2 = 0

a= 21; b = -11; c = -2

Δ = b² - 4ac

Δ = (-11)² - 4 . 21 . (-2)

Δ = 121 + 168

Δ = 289

x = (-b ± √Δ)/2a

x = ( - (-11) ± √289)/2 . 21

x = (11 ± 17)/42

x' = (11 + 17)/42

x' = (28)/42

x' = 2/3

x'' = (11 - 17)/ 42

x = -6/ 42

x'' = -1/7

S = {(-1/7, 2/3)}

c)

(2x + 1)(x - 1) = 2

2x² - 2x + x - 1 - 2 = 0

2x² - x - 3 = 0

a= 2; b = -1; c = -3

Δ = b² - 4ac

Δ = (-1)² - 4 . 2 . (-3)

Δ = 1 + 24

Δ = 25

x = (-b ± √Δ)/2a

x = ( - (-1) ± √25)/2 . 2

x = (1 ± 5)/4

x' = (1 + 5)/4

x' = (6)/4

x' = 3/2

x'' = (1 - 5)/ 4

x = -4/ 4

x'' = -1

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