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If p(x) and q(x) are arbitrary polynomials of degree at most 2, then the mapping =p(−1)q(−1)+p(0)q(0)+p(2)q(2)...

If p(x) and q(x) are arbitrary polynomials of degree at most 2, then the mapping

=p(−1)q(−1)+p(0)q(0)+p(2)q(2) defines an inner product in P3. Use this inner product to find

, ||p||, ||q||, and the angle θ between p(x) and q(x) for p(x)=2x^2+3 and q(x)=2x^2−6x.

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