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2) Resolva as seguintes equações do 2º grau.
a) x2 - 8x + 12 = 0
b) x2 + 2x -8= 0
•
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
Soluções para a tarefa
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!