Determine all polynomials

satisfying

for all .

Results 1 to 2 of 2

- Jun 24th 2009, 03:10 PM #1

- Joined
- Nov 2006
- Posts
- 152

- Jun 24th 2009, 04:55 PM #2
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.