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Suppose experimental data are represented by a set of points in the plane. An interpolating polynomial for the data is a polynomial whose graph passes through every point. In scientific work, such a polynomial can be used, for example, to estimate values between the known data points. Another use is to create curves for graphical images on a computer screen. One method for finding an interpolating polynomial is to solve a system of linear equations. Find the interpolating polynomial p(t) = a + a₁t+ a₂t for the data (1,12). (2.15). (3,16). That is, find ao. a₁, and a₂ such that the following is true. 2 ao + a₁ (1) + a₂(1)² = 12 ao+a₁ (2) + a₂ (2)² = 15 ao+a₁ (3) + a₂ (3)² = 16 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. 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.

Suppose experimental data are represented by a set of points in the plane. An interpolating polynomial for the data is a polynomial whose graph passes through every point. In scientific work, such a polynomial can be used, for example, to estimate values between the known data points. Another use is to create curves for graphical images on a computer screen. One method for finding an interpolating polynomial is to solve a system of linear equations. Find the interpolating polynomial p(t) = a + a₁t+ a₂t for the data (1,12). (2.15). (3,16). That is, find ao. a₁, and a₂ such that the following is true. 2 ao + a₁ (1) + a₂(1)² = 12 ao+a₁ (2) + a₂ (2)² = 15 ao+a₁ (3) + a₂ (3)² = 16 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. 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.

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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Suppose experimental data are represented by a set of points in the plane. An interpolating polynomial for the data is a polynomial whose graph passes through every point. In scientific work, such a polynomial can be used, for example, to estimate values between the known data points. Another use is to create curves for graphical images on a computer screen. One method for finding an interpolating polynomial is to solve a system of linear equations. Find the interpolating polynomial p(t) = a + a₁t+ a₂t for the data (1,12). (2,15). (3,16). That is, find ao. a₁, and a₂ such that the following is true. 2 ao + a₁ (1) + a₂(1)² = 12 ao+a₁ (2) + a₂ (2)² = 15 ao+a₁ (3) + a₂ (3)² = 16 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. 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.
Transcribed Image Text:Suppose experimental data are represented by a set of points in the plane. An interpolating polynomial for the data is a polynomial whose graph passes through every point. In scientific work, such a polynomial can be used, for example, to estimate values between the known data points. Another use is to create curves for graphical images on a computer screen. One method for finding an interpolating polynomial is to solve a system of linear equations. Find the interpolating polynomial p(t) = a + a₁t+ a₂t for the data (1,12). (2,15). (3,16). That is, find ao. a₁, and a₂ such that the following is true. 2 ao + a₁ (1) + a₂(1)² = 12 ao+a₁ (2) + a₂ (2)² = 15 ao+a₁ (3) + a₂ (3)² = 16 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. 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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