Question

17. Determine os zeros das funções definidas a seguir.
a) f(x) = x2 + 12x
b) g(x) = x2 + 4x + 3
c) h(x) = x2 – 25
d) i(x) = x2 – 8x
e) j(x) = x2 – x
f) k(x) = x2 – 20x + 64​

Answer 1

Explicação passo-a-passo:

a) f(x) = x2 + 12x

x.(x+12)=0

x=0

x+12=0

x=-12

S={( 0 ,-12)}

b) g(x) = x2 + 4x + 3

∆=b²-4.a.c

∆=(4)²-4.(1).(3)

∆=16-12

∆=4

x'=[-(+4)+√4]/2.(1)

x'=[-4+2]/2

x'=-2/2

x'=-1

x"=[-(+4)-√4]/2.(1)

x"=[-4-2]/2

x"=-6/2

x"=-3

S={( -3 , -1)}

c) h(x) = x2 – 25

x²-25=0

x²=25

x=√25

x=±5

S={( -5 , +5)}

d) i(x) = x2 – 8x

x.(x-8)=0

x=0

x-8=0

x=8

S={( 0 , 8)}

e) j(x) = x2 – x

x.(x-1)=0

x=0

x-1=0

x=1

S={( 0 , 1)}

f) k(x) = x2 – 20x + 64

∆=b²-4.a.c

∆=(-20)²-4.(1).(64)

∆=400-256

∆=144

x'=[-(-20)+√144]/2.(1)

x'=[20+12]/2

x'=32/2

x'=16

x"=[-(-20)-√144]/2.(1)

x"=[20-12]/2

x"=8/2

x"=4

S={( 16 , 4)}