how do you solve 3t^6-48t^2=0

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how do you solve 3t^6-48t^2=0

Mathematics
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Factor out 3t^2
3t^2(t^4-16)
factor 3t^2(t^4 - 16) = 0 t = 0 , 2 , -2

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Other answers:

Now you have the difference of two squares. Factor that.
How do you factor that out? I understand how you get that but there should be six answers
t = 0 , 2 , -2, 2i,-2i
\[t^4-16=(t^2-4)(t^2+4)=(t-2)(t+2)(t^2+4)\]
what happened to the 3t^2?
x=0 double root
I left it off because I thought you already recognized that it is a factor.
so how do you get the six answers by factoring is what im confused about
\[3t^2(t-2)(t+2)(t^2+4)\]
That is the completely factored form.
\[x_1=0,x_2=0,x_3=2,x_4=-2,x_5=2i,x_6=-2i\]
how do you get the six answers though. I know there should be six because the degree is six
there are 6 answers already!
How didyou get them though? I see and understand there are six but i dont know HOW you got them
\[3t^6-48t^2=0\] \[3t^2(t^4-16)=0\] \[3t^2(t-2)(t+2)(t^2+4)=0\]
If the product of factors is 0 then one of the factors has to be 0. so set each factor to 0 and solve
  • phi
not sure how you are confused. Do you know how to find the *2* roots of \[ t^2= 0\] t= ±0 two solutions, 0 and 0
\[3t^2=0\] \[t+2=0\] \[t-2=0\] \[t^2+4=0\]
if a*b=0 then a=0 or b=0
Okay, now I understand, thankyou so much

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