Suppose q ∈ P(IR). Prove that there exists a polynomial p ∈ P(IR) such that q(x) = (x² – 3x)p''(x) + (2x - 3)p'(x) + p(0).
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Step 1
This means that q(x) can be written as q(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, where a_n, a_{n-1}, ..., a_1, a_0 are real numbers and a_n ≠ 0. Show more…
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