Prove that there is only one polynomial P3(x) among all polynomials of degree < 3 that satisfy the interpolating conditions 11. (а) P3(x;) = yi, i = 0, 1, 2, 3 where the x;'s are distinct. Hint: Generalize the proof given in and following (4.10) for the uniqueness of P2(x). (b) Give a proof of uniqueness for P(x) in Theorem 4.1.5.

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A: Here, given that the polynomial p(x) is divisible by (x-a)n. So, p(x)=(x-a)nq(x)...(1) Where, q(x)…

Q: 10. Write a third-degree polynomial f(x) with integer coefficients and zeros of 5, -, and 4.

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A:

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A: To form: The interpolating polynomial of degree k that satisfies pjx0=fjx0 for 0≤j≤k

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Q: n 5. Let n be a fixed positive integer. Denote by Po the set of all real polynomials of degree n or…

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A: Note: According to bartleby we have to answer only first three subparts please upload the question…

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Q: Consider the following. 3x4 - 8x + 5 = 0, [2, 3) (a) Explain how we know that the given equation…

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A: Our objective is given below:

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A: Hello. Since your question has multiple parts, we will solve the first parts for you. If you want…

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A: In this question , use the given values and solve the equations and find the polynomial.

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A: From Einstein criteria we sole this