
#1
Mar208, 07:56 PM

P: 239

1. The problem statement, all variables and given/known data
Prove that if p(x)=anx^n +an1x^n1+..........a0, where a0,.........., "an" ε reals, is a polynomial, then p can have at most n roots. 2. Relevant equations 3. The attempt at a solution C ε R is a root of a polynomial p if p(c)=0. If c is a root of p, then xc is a factor of p. I'm not sure where to go from here. I think it would probably be the easiest to prove this by proving the contrapositive as being false. Could someone please give me a hint or show me where to go from here? Thank you very much 



#2
Mar208, 09:45 PM

Sci Advisor
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Thanks
P: 25,171

Sure. Suppose the polynomial has n+1 different roots. c1,c2,...cn+1. Since c1 is a root the polynomial p(x) can be factored (xc1)*p1(x) where p1 has degree n1. The other c's must be roots of p1(x) since they aren't roots of (xc1). Continue in this way until you reach degree 1. Now you have a linear polynomial with two different roots. Possible?




#3
Mar208, 10:26 PM

P: 239

Thank you very much
Would it be somthing like this? (p1x)^(n1)(xc2)(xc3)^(n) Thank you 



#4
Mar208, 10:38 PM

Sci Advisor
HW Helper
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P: 25,171

proving a formula
No, that's not clear at all. Start by proving if n=1 then the polynomial can't have 2 roots. Ok?




#5
Mar508, 10:10 PM

P: 239

Thank you very much
Regards 


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