Determine all polynomials

satisfying

for all .

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- Jun 24th 2009, 02:10 PMperashf(x)
Determine all polynomials

satisfying

for all . - Jun 24th 2009, 03:55 PMTheAbstractionist
When the RHS = 0 so the LHS must be 0 as well; thus

Substituting then gives RHS = 0 again, so LHS must be 0

Continuing this way, we get Hence must have these five roots and so we have

where is some polynomial.

Thus the polynomial must satisfy for all and so must be a constant function. Hence

where is a real constant.