Question

Resolva as seguintes equações do 2º grau e determine as raízes se existir.

a) -16x²+49=0
b )6x²+x-1=0
c )2x²-7x=15
d) 4x²+9=12x
e) x²=x+12
f) 2x²=-12x-18
g) x²+9=4x
h) 25x²=20x-4
i) 2x=15-x²
j )x²+3x-6=-8
k) x²+x-7=5
m) 4x²-x+1=x+3x²
n) 3x²+5x=-x-9+2x²
o) 4+x (x-4)=x

PESSOAL POR FAVOR ME AJUDEM NO MEU TRABALHO?!

Answer 1

a) -16x^2+49=0
-16x^2=0-49
-16x^2=-49.(-1)
16x^2=49
x^2=49/16
x^2=3.0625
x= raiz de 3.0625
x=-/+ 1,75
b) 6x^2+x-1=0
delta=b^2-4ac
delta=1^2-4.6.(-1)
delta=1+24
delta=25
x=-b-/+ raiz de delta/2a
x=-1-5/2.6
x=-6/12 (÷6)
x=-1/2
x=-1+5/2.6
x=4/12 (÷4)
x=1/3
c) 2x^2-7x=15
2x^2-7x-15=0
delta=b^2-4ac
delta=(-7)^2-4.2.(-15)
delta=49+120
delta=169
x=-b-/+ raiz de delta/2a
x=-(-7)-13/2.2
x=7-13/4
x=6/4 (÷2)
x=3/2
x=-(-7)+13/2.2
x=7+13/4
x=20/4
x=5
d) 4x^2+9=12x
4x^2-12x+9=0
delta=b^2-4ac
delta=(-12)^2-4.4.9
delta=144-144
delta=0
x=-b-/+ raiz de delta/2a
x=-(-12)-0/2.4
x=12-0/8
x=12/8 (÷4)
x=3/2
e) x^2=x+12
x^2-x-12=0
delta=b^2-4ac
delta=(-1)^2-4.1.(-12)
delta=1+48
delta=49
x=-b-/+ raiz de delta/2a
x=-(-1)-7/2.1
x=1-7/2
x=-6/2
x=-3
x=-(-1)+7/2.1
x=1+7/2
x=8/2
x=4
f) 2x^2=-12x-18
2x^2+12x+18=0
delta=b^2-4ac
delta=12^2-4 2.18
delta=144-144
delta=0
x=-b-/+ raiz de delta/2a
x=-12-0/2.2
x=-12/4
x=-3
g) x^2+9=4x
x^2-4x+9=0
delta=b^2-4ac
delta=(-4)^2-4.1.9
delta=16-36
delta=-20
delta negativo, não há raízes reais
h) 25x^2=20x-4
25x^2-20x+4=0
delta=b^2-4ac
delta=(-20)^2-4.25.4
delta=400-400
delta=0
x=-b-/+ raiz de delta/2a
x=-(-20)-0/2.25
x=20-0/50
x=20/50 (÷5)
x=4/10
i) 2x=15-x^2
x^2+2x-15=0
delta=b^2-4ac
delta=2^2-4.1.(-15)
delta=4+60
delta=64
x=-b-/+ raiz de delta/2a
x=-2-8/2.1
x=-10/2
x=-5
x=-2+8/2.1
x=6/2
x=3
j) x^2+3x-6=-8
x^2+3x-6+8
x^2+3x+2=0
delta=b^2-4ac
delta=3^2-4.1.2
delta=9-8
delta=1
x=-b-/+ raiz de delta/2a
x=-3-1/2.1
x=-4/2
x=-2
x=-3+1/2.1
x=-2/2
x=-1
k) x^2+x-7=5
x^2+x-7-5
x^2+x-12=0
delta=b^2-4ac
delta=1^2-4.1.(-12)
delta=1+48
delta=49
x=-b-/+ raiz de delta/2a
x=-1-7/2.1
x=-8/2
x=-4
x=-1+7/2.1
x=6/2
x=3
m) 4x^2-x+1=x+3x^2
4x^2-3x^2-x-x+1
x^2-2x+1=0
delta=b^2-4ac
delta=(-2)^2-4.1.1
delta=4-4
delta=0
x=-b-/+ raiz de delta/2a
x=-(-2)-0/2.1
x=2-0/2
x=2/2
x=1
n) 3x^2+5x=-x-9+2x^2
3x^2-2x^2+5x+x+9
x^2+6x+9=0
delta=b^2-4ac
delta=6^2-4.1.9
delta=36-36
delta=0
x=-b-/+ raiz de delta/2a
x=-6-0/2.1
x=-6/2
x=-3
o) 4+x.(x-4)=x
4+x^2-4x=x
4+x^2-4x-x
x^2-4x-x+4
x^2-5x+4=0
delta=b^2-4ac
delta=(-5)^2-4.1.4
delta=25-16
delta=9
x=-b-/+ raiz de delta/2a
x=-(-5)-3/2.1
x=5-3/2
x=2/2
x=1
x=-(-5)+3/2.1
x=5+3/2
x=8/2
x=4