Polynomials

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SANZEED
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Polynomials

Unread post by SANZEED » Thu Jan 26, 2012 7:20 am

The polynomial $P(x)$ satisfies the following condition,
$P(2x^{2}-1) =( P(x)^{2}/2)-1$
What is the difference between the highest and lowest value of $P(x)$? Note that more than one such polynomials exists.
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Phlembac Adib Hasan
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Re: Polynomials

Unread post by Phlembac Adib Hasan » Thu Jan 26, 2012 11:46 am

Hint :
First find out enough information to find first and second derivative of $P(x)$.Then it's simple exercise of maxima-minima.
Comment:The topic should be moved to Algebra.I used calculus.If anyone finds other solves, please post here.
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