Question

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2) Resolva as seguintes equações do 2º grau.
a) x2 - 8x + 12 = 0
b) x2 + 2x -8= 0
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c) 2x2 – 8x + 8 = 0
d) x2 - 4x - 5 = 0
e) -x2 + x + 12 = 0
f) -x2 + 6x - 5 = 0
g) 2x2 - 7x - 15 = 0
h) 4x2 - 12x + 9 = 0
i) x2 - x - 12 = 0
j) 2x2 + 12x + 18 = 0

Answer 1

2) Resolva as seguintes equações do 2º grau.

a) x2 - 8x + 12 = 0

a=1

b=-8

c=12

∆=b²-4.a.c

∆=(-8)²-4.(1).(12)

∆=64-48

∆=16

x'=-(-8)+√16/2=8+4/2=12/2=6

x"=-(-8)-√16/2=8-4/2=4/2=2

S={6,2}

b) x2 + 2x -8= 0

a=1

b=2

c=-8

∆=b²-4.a.c

∆=(2)²-4.(1).(-8)

∆=4+32

∆=36

x'=-2+√36/2=-2+6/2=4/2=2

x"=-2-√36/2=-2-6/2=-8/2=-4

s={2,-4}

c) 2x2 – 8x + 8 = 0

a=2

b=-8

c=8

∆=b²-4.a.c

∆=(-8)²-4.(2).(8)

∆=64-64

∆=0

x'=x"=-(-8)/2.(2)

x'=x"=8/4

x'=x"=2

S={2}

d) x2 - 4x - 5 = 0

a=1

b=-4

c=-5

∆=b²-4.a.c

∆=(-4)²-4.(1).(-5)

∆=16+20

∆=36

x'=-(-4)+√36/2=4+6/2=10/2=5

x"=-(-4)-√36/2=4-6/2=-2/2=-1

S={-1,5}

e) -x2 + x + 12 = 0

a=-1

b=1

c=12

∆=b²-4.a.c

∆=(1)²-4.(-1).(12)

∆=1+48

∆=49

x'=-1+√49/-2=-1+7/-2=6/-2=-3

x"=-1-√49/-2=-1-7/-2=-8/-2=4

S={-3,4}

f) -x2 + 6x - 5 = 0

a=-1

b=6

c=-5

∆=b²-4.a.c

∆=(6)²-4.(-1).(-5)

∆=36-20

∆=16

x'=-6+√16/-2=-6+4/-2=-2/-2

x"=-6-√16/-2=-6-4/-2=-10/-2=5

S={-2,5}

g) 2x2 - 7x - 15 = 0

a=2

b=-7

c=-15

∆=b²-4.a.c

∆=(-7)²-4.(2).(-15)

∆=49+120

∆=169

x'=7+√169/4=7+13/4=20/4=5

x"=7-√169/4=7-13/4=6/4=3/2

S={3/2,5}

h) 4x2 - 12x + 9 = 0

a=4

b=-12

c=9

∆=b²-4.a.c

∆=(-12)²-4.(4).(9)

∆=144-144

∆=0

x'=x"=-(-12)/2.(4)

x'=x"=12/8

x'=x"=6/4

x'=x"=3/2

i) x2 - x - 12 = 0

a=1

b=-1

c=-12

∆=b²-4.a.c

∆=(-1)²-4.(1).(-12)

∆=1+48

∆=49

x'=1+√49/2=1+7/2=8/2=4

x"=1-√49/2=1-7/2=-6/2=-3

S={-3,4}

j) 2x2 + 12x + 18 = 0

a=2

b=12

c=18

∆=b²-4.a.c

∆=(12)²-4.(2).(18)

∆=144-144

∆=0

x'=x"=12/2.(2)

x'=x"=12/4

x'=x"=3

S={2}

espero ter ajudado!

boa tarde!