SOLUTION: find all solutions by factoring: 4t^6-t^4=0

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Question 541523: find all solutions by factoring: 4t^6-t^4=0
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Find all solutions: (You should expect to get 6 solutions, some of which might be identical)
4t%5E6-t%5E4+=+0 Factor out t%5E4
t%5E4%28t%5E2-1%29+=+0 Apply the "zero product rule".
t%5E4+=+0 or t%5E2-1+=+0
If t%5E4+=+0 then t%2At%2At%2At+=+0 and t+=+0 is a solution four times.
4t%5E2-1+=+0 Factor this.
%282t%2B1%29%282t-1%29+=+0 Apply the "zero product rule"'
2t%2B1+=+0 or 2t-1+=+0 so...
2t+=+-1 and t+=+-1%2F2
2t+=+1 and t+=+1%2F2
The six solutions (four of which are identical) are:
t+=+0
t+=+0
t+=+0
t+=+0
t+=+-1%2F2
t+=+1%2F2
To give some idea of the graphical soltions:
graph%28400%2C400%2C-3%2C3%2C-5%2C5%2C4x%5E6-x%5E4%29