If has multiple roots. Prove that
Umm... I just cant prove that..... is the question wrong or am i doing something wrong =S?
thanks in advance.
Hello,
I'll try. I did it on a paper and just noticed a tiny mistake, so I'll go freely while typing lol ! But you gotta check it because I'm sure I won't get the result you're given
If P(x) has multiple roots (one or more or all roots are multiple ?), then there exists m such that
(1) and (2)
From (2), we get or
If m=0, then b=0 by (1).
Let's say otherwise that's not funny
So
Substituting in (1) :
Take the 3rd power of both sides :
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Remember that
We have (I write it in the same order so that you can see) :
and
and similarly
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Which is too similar to be a big mistake