Question

Resolva as equações do 2º grau em R. a) x² + 10x + 25 = 0 b) - x² + 12x - 20 = 0 c) 2x² + 3x + 1 = 0 d) x² - 3x + 10 = 0 e) - x²- x + 30 = 0 f ) x² - 2x + 1 = 0​

Answer 1

Explicação passo-a-passo:

a)

x²+10x+25=0

a=1, b=10, c=25

∆=b²-4.a.c

∆=10²-4.1.25

∆=100-100=0

x=-b±√∆/2.a

x=-10/2=-5

b)

-x²+12x-20=0

a=-1, b=12, c=-20

∆=b²-4.a.c

∆=12²-4.(-1).(-20)

∆=144-80=64

x=-b±√∆/2.a

x'=-12+√64/2.(-1)=-12+8/-2=-4/-2=2

x"=-12-√64/2.(-1)=-12-8/-2=-20/-2=10

c)

2x²+3x+1=0

∆=3²-4.2.1

∆=9-8=1

x'=-3+1/2.2=-2/4=-1/2

x"=-3-1/4=-4/4=-1

d)

x²-3x+10=0

∆=(-3)²-4.1.10

∆=9-40=-31

S=∅

e)

-x²-x+30=0

∆=(-1)²-4.(-1).30

∆=1+120=121

x'=1+√121/2.(-1)=1+11/-2=12/-2=-6

x"=1-11/-2=-10/-2=5

f)

x²-2x+1=0

∆=(-2)²-4.1.1=4-4

∆=0

x=-(-2)/2.1=2/2=1