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Find the interpolating polynomial p(t) = a0 + a1t + a2t2 for the data (1, 14), (2, 18), (3, 20). That is, find a0, a1, and a2 such that the following is true. a0 +a1(1) + a2(1)1  = 14 a0 +a1(2) + a2(2)2 = 18 a0 + a1(3) + a2(3)2 = 20

Find the interpolating polynomial p(t) = a0 + a1t + a2t2 for the data (1, 14), (2, 18), (3, 20). That is, find a0, a1, and a2 such that the following is true. a0 +a1(1) + a2(1)1  = 14 a0 +a1(2) + a2(2)2 = 18 a0 + a1(3) + a2(3)2 = 20

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find the interpolating polynomial p(t) = a0 + a1t + a2t2 for the data (1, 14), (2, 18), (3, 20). That is, find a0, a1, and a2 such that the following is true.

a0 +a1(1) + a2(1)1  = 14

a0 +a1(2) + a2(2)2 = 18

a0 + a1(3) + a2(3)2 = 20

 

If necessary, select the correct choice below and fill in the answer box to complete your choice.

O A. The interpolating polynomial is p(t) = ___ .

O B. There are infinitely many possible interpolating polynomials.

O C. There does not exist an interpolating polynomial for the given data.

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