Question

me ajuda nessa aqui fazendo favor: a) x(x+1)=0 b) 2x(x-5)=0 c) (x+3)(x-1)=0 d) (x-6)(4x-8)=0

Answer 1

Boa noite!
A)
X(X+1)=0
x²+x=0
a=1, b=1, c=0
Δ = b²-4ac
Δ = 1²-4.1.0
Δ = 1-0 = 0
X = -b+-√Δ/2a
X = -1+-√0/2.1
X = -1+-0/2
X' = -1-0/2 = -1/2
X" = -1+0/2 = -1/2
S = {(-1/2, -1/2)}

B)
2X(X-5)=0
2X²-10X=0
a=2, b=-10, c=0
Δ = b²-4ac
Δ = (-10)²-4.2.0
Δ = 100

X=-b+-√Δ/2a
X=-(-10)+-√100/2.2
X=10+-10/4
X'=10-10/4 = 0
X"=10+10/4= 20/4 = 5
S={(0,5)}

C)
(x+3)(x-1)=0
x²-x+3x-3=0
X²+2X-3=0
a=1, b=2, c=-3
Δ = b²-4ac
Δ = 2²-4.1.(-3)
Δ = 4+12
Δ = 16
X= -b+-√Δ/2a
X= -2+-√16/2.1
X= -2+-4/2
X'=-2-4/2 = -6/2 = -3
X"=-2+4/2 = 2/2 = 1
S={(-3, 1)}

D)
(x-6)(4x-8)=0
4x²-8x-24x+48=0
4x²-32x+48=0  (simplificando por 4)
x²-8x+12=0
a=1, b=-8, c= 12
Δ = b²-4ac
Δ = (-8)²-4.1.12
Δ = 64 - 48
Δ = 16
X= -b+-√Δ/2a
X= -(-8)+-√16/2.1
X= 8+-4/2
X'=8-4/2= 4/2 = 2
X"=8+4/2= 12/2 = 6
S={(2, 6)}

Espero ter ajudado  ;)