Question

me ajuda pfv3) Calcule a discriminante ∆ nas equações abaixo: ( 1,0 )
a) x² - 8x + 7 = 0
b) 3x² - 15x + 12 =0
c) x² - 5x + 6 = 0
d) x² + 9x + 8 = 0
e) 5x² - 3x – 2 = 0

Answer 1

a) x² - 8x + 7 = 0

A = 1 B = -8 C = 7

∆ = b² - 4ac

∆ = (-8²) - 4 (1) (7)

∆ = 64 - 28

∆ = 36

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x = -b ± √∆

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2a

x = - (-8) ± √36

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2•1

x= 8 ± 6

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2

x1= 8+6 /2= 7

x2= 8-6 /2= 2

b) 3x² - 15x + 12 = 0

A = 3 B = -15 C = 12

∆ = (-15²) - 4 (3) (12)

∆ = 225 - 144

∆ = 81

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x = -(-15) ± √81

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2•3

x = 15 ± 9

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6

x1= 15+9 /6 = 4

x2= 15-9 /6 = 1

c) x² - 5x + 6 = 0

A = 1 B = -5 C = 6

∆ = (-5²) - 4 (1) (6)

∆ = 25 - 24

∆ = 1

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x = -(-5) ± √1

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2•1

x= 5±1

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2

x1= 5+1 /2 = 3

x1= 5-1 /2 = 2

d) x² + 9x + 8 = 0

A = 1 B = 9 C = 8

∆ = 9² - 4 (1) (8)

∆ = 81 - 32

∆ = 49

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x = -9 ± √49

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2•1

x = -9 ± 7

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2

x1= -9 + 7 /2 = -1

x2= -9 - 7 /2 = 8

e) 5x² - 3x - 2 = 0

A = 5 B = -3 C = -2

∆ = (-3²) - 4 (5) (-2)

∆ = 9 + 40

∆ = 49

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x = -(-3) ± √49

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2•5

x = 3 ± 7

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10

x1= 3+7 /10 = 1

x2= 3-7 /10 = --