Question

6. (0.9) Resolva através da formula de Baskara a) 2x'2- 8x + 8 = 0 b) X'2 -4x - 5 = 0 c) -x'2 + x + 12= 0​

Answer 1

a) 2x² - 8x + 8 = 0

a = 2

b = -8

c = 8

Δ = b² - 4 . a . c

Δ = (-8)² - 4 . 2 . 8

Δ = 64 - 8 . 8

Δ = 64 - 64

Δ = 0

x = -b ± √Δ 2 . a

x = -(-8) ± √0 /2 . 2

x = 8 ± 0 /4

x' = 8 - 0 /4

x' = 8/4

x' = 2

x" = 8 + 0 /4

x" = 8/4

x" = 2

x" = 2

S = { 2 , 2 }

b) x² - 4x - 5 = 0

a = 1

b = -4

c = -5

Δ = b² - 4 . a . c

Δ = (-4)² - 4 . 1 . (-5)

Δ = 16 - 4 . (-5)

Δ = 16 - (-20)

Δ = 16 + 20

Δ = 36

x = -b ± √Δ /2 . a

x = -(-4) ± √36 /2 . 1

x = 4 ± 6 /2

x' = 4 - 6 /2

x' = -2/2

x' = -1

x" = 4 + 6 /2

x" = 10/2

x" = 5

x" = 5

S = { -1 , 5 }

c) -x² + x + 12 = 0

a = -1

b = 1

c = 12

Δ = b² - 4 . a . c

Δ = 1² - 4 . (-1) . 12

Δ = 1 - 4 . (-12)

Δ = 1 - (-48)

Δ = 1 + 48

Δ = 49

x = -b ± √Δ /2 . a

x = -1 ± √49 /2 . (-1)

x = -1 ± 7 /-2

x' = -1 - 7 /-2

x' = -8/-2

x' = 4

x" = -1 + 7 /-2

x" = 6/-2

x" = -3

x" = -3

S = { 4 , -3 }