Question

Determine as raizes de cada equação do segundo grau:
a) x2-3x+5=0
b) -x2+4x=0
c) 3x2-6x+3=0
d) x2-6x=0
e) x2+4x+4=0
f) 2x2-10x+8=0
g) x2-12x+36=0

Answer 1

a) x^2-3x+5=0
delta=b^2-4ac
delta=(-3)^2-4.1.5
delta=9-20
delta=-11
delta negativo, não há raízes reais
b) -x^2+4x=0
delta=b^2-4ac
delta=4^2-4.(-1).0
delta=16+0
delta=16
x=-b-/+ raiz de delta/2a
x=-4-4/2.(-1)
x=-8/-2
x=4
x=-4+4/2.(-1)
x=0/-2
x=0
c) 3x^2-6x+3=0
delta=b^2-4ac
delta=(-6)^2-4.3.3
delta=36-36
delta=0
x=-b-/+ raiz de delta/2a
x=-(-6)-0/2.3
x=-6-0/6
x=-6/6
x=-1
d) x^2-6x=0
x(x-6)=0
x=0
x-6=0
x=0+6
x=6
e) x^2+4x+4=0
delta=b^2-4ac
delta=4^2-4.1.4
delta=16-16
delta=0
x=-b-/+ raiz de delta/2a
x=-4-0/2.1
x=-4/2
x=-2
f) 2x^2-10x+8=0
delta=b^2-4ac
delta=(-10)^2-4.2.8
delta=100-64
delta=36
x=-b-/+ raiz de delta/2a
x=-(-10)-6/2.2
x=10-6/4
x=4/4
x=1
x=-(-10)+6/2.2
x=10+6/4
x=16/4
x=4
g) x^2-12x+36=0
delta=b^2-4ac
delta=(-12)^2-4.1.36
delta=144-144
delta=0
x=-b-/+ raiz de delta/2a
x=-(-12)-0/2.1
x=12-0/2
x=12/2
x=6

Answer 2

x²-3x+5=0 a=1, b=-3, c=5
∆=(-3)²-4*1*5
∆=9-20
∆=-11
impossível raíz real para delta com números negativos...

b)-x²+4x=0 a=-1, b=4
∆=4²-4*-1*0
∆=16

x=(-4±√16)/2*(-1)
x=(-4±4)-2
x'=(-4+4)/-2
x'=0/-2
x'=0
x"=(-4-4)/-2
x"=-8/-2
x"=4

c)3x²-6x+3=0 a=3,b=-6,c=3
∆=-6²-4*3*3
∆=36-36
∆=0
x=(-(-6)±√0)/2*3
x=(6±0)/6
x' e x" = 6/6
x' e x" = 1

d)x²-6x=0 a=1, b=-6,c=0

∆=-6²-4*1*0
∆=36

x=(-(-6)±√36)/2*1
x=(6±6)/2
x'=(6+6)/2
x'=12/2
x'=6
x"=(6-6)/2
x"=0/2
x"=0

e) x²+4x+4=0 a=1, b=4, c=4
∆=4²-4*1*4
∆=16

x=(-4±√16)/2*1
x=(-4±4)/2
x'=(-4+4)/2
x'=0/2
x'=0
x"=(-4-4)/2
x"=-8/2
x"=-4

f) 2x²-10x+8=0 a=2, b=-10,c=8

∆= -10²-4*2*8
∆= 100-64
∆= 36

x=(-(-10)±√36)/2*2
x=(10±6)/4
x'=(10+6)/4
x'=16/4
x'=4
x"=(10-6)/4
x"=4/4
x"=1

g)x²-12x+36=0 a=1, b=-12,c=36

∆=-12²-4*1*36
∆=144-144
∆=0

x=(-(-12)±√0)/2*1
x=(12±0)/2
x' e x" =12/2
x' e x" =6