$\displaystyle Let V be $\displaystyle R_{2}[x] $, and let S be the subspace of all polynomials p(x) satisfying

$\displaystyle \\ \frac{\2d^2\p}{dx^2} = p(2)$

Find the orthogonal complement of S with respect to the inner product

<p,q> = p(-1)q(-1) +p(0)q(0) + p(1)q(1)

And find the polynomial in S which is closest to 1 + x _ x^2

Thanks for any help.

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