Question

sem resolver as equaçoes determine quais tem raizes reais.
a)4.(x2+2)=8.(x+1)

b)x2-3.(x-15)=-4-3x

c)3x.(x-1)=2x

d)-6x2+12=0

e)-8x2-32=16

f)11x2=0

Answer 1

a) 4.(x^2+2)=8(x+1)
4x^2+8=8x+8
4x^2-8x+8-8=0
4x^2-8x=0
2x(2x-4)=0
2x=0》x=0/2》x=0
2x-4=0》2x=4》x=4/2》x=2

b) x^2-3.(x-15)=4-3x
x^3-15x^2-3x+45=4-3x
x^3 - 15x^2 -3x + 3x +45- 4 =0
x^3 - 15x^2 + 0x + 41 =0

c) 3x(x-1)=2x
3x^2-3x=2x
3x^2 - 3x - 2x=0
3x^2 -5x=0
x(3x-5)=0
x=0
3x-5=0》3x=5》x=5/3

d) -6x + 12 =0
-6x(x+2)=0
-6x=0》x=0/6》x=0
x+2=0》x=-2

e) -8x^2 - 32 =16
-8x^2 -32 - 16 = 0
-8x^2 - 48 = 0
-8x(x-6)=0
-8x=0》x=0/8》x=0
x-6=0》x=6

f) 11x^2=0
x(11x)=0
x=0
11x=0》x=0/11》x=0