Let p(x) = 2 x x2 and q(x) = 1 + x + x2. Using the inner product a0 + a1x + a2x2, b0 +

Chapter 5, Problem 19

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Let p(x) = 2 x x2 and q(x) = 1 + x + x2. Using the inner product a0 + a1x + a2x2, b0 + b1x + b2x2 = a0b0 + a1b1 + a2b2, find all polynomials r(x) = a + bx + cx2 in P2(R) such that {p(x), q(x),r(x)} is an orthogonal set.

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