Question

Responda utilizando a fórmula base:
X = - b ± √b² -4 .a.c / 2.a
a) 3x²-2x-1=0
b) x²-7x+6=0
c) 4x²-12x+9=0
d) -x²-2x+15=0
e) x²-6x+9=0
f) 7x²+28x+21=0

Me ajudem!!!

Answer 1

a) 3x² - 2x - 1 = 0

a = 3

b = -2

c = -1

Δ = b²- 4 . a . c

Δ = (-2)² - 4 . 3 . (-1)

Δ = 4 - (-12)

Δ = 4 + 12

Δ = 16

x = -b ± √Δ /2 . a

x = -(-2) ± √16 /2 . 3

x = 2 ± 4 /6

x' = 2 - 4 /6

x' = -2/6

x' = -1/3

x" = 2 + 4 /6

x" = 6/6

x" = 1

S = { -1/3 , 1 }

b) x² - 7x + 6 = 0

a = 1

b = -7

c = 6

Δ = b²- 4 . a . c

Δ = (-7)² - 4 . 1 . 6

Δ = 49 - 24

Δ = 25

x = -b ± √Δ /2 . a

x = -(-7) ± √25 /2 . 1

x = 7 ± 5 /2

x' = 7 - 5 /2

x' = 2/2

x' = 1

x" = 7 + 5 /2

x" = 12/2

x" = 6

S = { 1 , 6 }

c) 4x² - 12x + 9 = 0

a = 4

b = -12

c = 9

Δ = b²- 4 . a . c

Δ = (-12)² - 4 . 4 . 9

Δ = 144 - 16 . 9

Δ = 144 - 144

Δ = 0

x = -b ± √Δ /2 . a

x = -(-12) ± √0 /2 . 4

x = 12 ± 0 /8

x' = 12 - 0 /8

x' = 12/8

x' = 3/2

x" = 12 + 0 /8

x" = 12/8

x" = 3/2

S = { 3/2 , 3/2 }

d) -x² - 2x + 15 = 0

a = -1

b = -2

c = 15

Δ = b²- 4 . a . c

Δ = (-2)² - 4 . (-1) . 15

Δ = 4 - (-60)

Δ = 4 + 60

Δ = 64

x = -b ± √Δ /2 . a

x = -(-2) ± √64 /2 . (-1)

x = 2 ± 8 /-2

x' = 2 - 8 /-2

x' = -6/-2

x' = 3

x" = 2 + 8 /-2

x" = 10/-2

x" = -5

S = { 3 , -5 }

e) x² - 6x + 9 = 0

a = 1

b = -6

c = 9

Δ = b²- 4 . a . c

Δ = (-6)² - 4 . 1 . 9

Δ = 36 - 36

Δ = 0

x = -b ± √Δ /2 . a

x = -(-6) ± √0 /2 . 1

x = 6 ± 0 /2

x' = 6 - 0 /2

x' = 6/2

x' = 3

x" = 6 + 0 /2

x" = 6/2

x" = 3

S = { 3 , 3 }

f) 7x² + 28x + 21 = 0

a = 7

b = 28

c = 21

Δ = b²- 4 . a . c

Δ = 28² - 4 . 7 . 21

Δ = 784 - 28 . 21

Δ = 784 - 588

Δ = 196

x = -b ± √Δ /2 . a

x = -28 ± √196 /2 . 7

x = -28 ± 14 /14

x' = -28 - 14 /14

x' = -42/14

x' = -3

x" = -28 + 14 /14

x" = -14/14

x" = -1

S = { -3 , -1 }