2. The general form of a cubic is p(x) = ao + a1x +a2x² + a3x³ %3D Suppose you are given the following four points in the x, y plane: (-1,4), (0, 1), (1,0), and (2, –5). Find a cubic passing through all these points. (Hint: if the cubic passes through these points, then p(-1) = 4, p(0) = 1, p(1) = 0, and p(2) = -5. Plug these values into the general form of a cubic and get a system of 4 equations with 4 unknowns: ao, a1, a2, a3. Solve this system using matrices.)
2. The general form of a cubic is p(x) = ao + a1x +a2x² + a3x³ %3D Suppose you are given the following four points in the x, y plane: (-1,4), (0, 1), (1,0), and (2, –5). Find a cubic passing through all these points. (Hint: if the cubic passes through these points, then p(-1) = 4, p(0) = 1, p(1) = 0, and p(2) = -5. Plug these values into the general form of a cubic and get a system of 4 equations with 4 unknowns: ao, a1, a2, a3. Solve this system using matrices.)
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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Transcribed Image Text:2. The general form of a cubic is
p(x) = ao + a1x + azx² + azx³
Suppose you are given the following four points in the x, y plane: (-1,4), (0, 1), (1,0),
and (2, –5). Find a cubic passing through all these points. (Hint: if the cubic passes
through these points, then p(-1) = 4, p(0) = 1, p(1) = 0, and p(2) = -5. Plug
these values into the general form of a cubic and get a system of 4 equations with 4
unknowns: ao, a1, a2, az. Solve this system using matrices.)
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