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Let $\mathcal{P}_{2}$ be the space of polynomials $p(x)=a+b x+c x^{2}$ of degree at most 2 with the inner product $\langle p, q\rangle=\int_{-1}^{1} p(x) q(x) d x$. Let $\ell$ be the functional $\ell(p):=p(0)$. Find $h \in \mathcal{P}_{2}$ so that $\ell(p)=\langle h, p\rangle$ for all $p \in \mathcal{P}_{2}$.
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