Question

Determine a solução das equações do 2o grau:

a) x^2 – 64
b) x^2 – 1 = 24
c) x^2 + 6x
d) x^2 – 7x + 14
e) x^2 + x - 6
f) x^2 + 3x – 10 = 0

Answer 1

Explicação passo-a-passo:

a)

x²-64=0

a=1, b=0, c=-64

∆=b²-4ac

∆=0²-4.1.(-64)

∆=0+256

∆=256

x=-b±√∆/2.a

x'=0+√256/2.1=16/2=8

x"=0-√256/2.1=-16/2=-8

b)

x²-1=24

x²-1-24=0

x²-25=0

∆=0²-4.1.(-25)

∆=0+100

∆=100

x=0±√100/2.1=10/2=5

x'=5, x"=-5

c)

x²+6x=0

a=1, b=6, c=0

∆=6²-4.1.0

∆=36-0

∆=36

x'=-6+√36/2.1=-6+6/2=0/2=0

x"=-6-√36/2.1=-6-6=2=-12/2=-6

d)

x²-7x+14=0

∆=(-7)²-4.1.14

∆=49-56

∆=-10

S=∅

e)

x²+x-6=0

a=1, b=1, c=-6

∆=1²-4.1.-6

∆=1+24

∆=25

x'=-1+√25/2.1=-1+5/2=4/2=2

x"=-1-√25/2.1=-1-5/2=-6/2=-3

f)

x²+3x-10=0

∆=3²-4.1.(-10)

∆=9+40

∆=49

x'=-3+√49/2.1=-3+7/2=4/2=2

x"=-3-√49/2.1=-3-7/2=-10/2=-5