= 12. (a) Find the unique quadratic polynomial y ax²+bx+c that passes through the three points (1, 1), (3,5), and (-2, 0) in the x-y plane. (Hint: this will involve a linear system where a, b, and c are the unknowns.) (b) How many data points (x, y) should be needed to uniquely determine the coefficients of an nth degree polynomial anxn+an-1xn−¹+...+a₁x+ao? Explain your answer in terms of linear systems.
= 12. (a) Find the unique quadratic polynomial y ax²+bx+c that passes through the three points (1, 1), (3,5), and (-2, 0) in the x-y plane. (Hint: this will involve a linear system where a, b, and c are the unknowns.) (b) How many data points (x, y) should be needed to uniquely determine the coefficients of an nth degree polynomial anxn+an-1xn−¹+...+a₁x+ao? Explain your answer in terms of linear systems.
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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12. (a) Find the unique quadratic polynomial y
ax²+bx+c that passes through
the three points (1, 1), (3,5), and (-2, 0) in the x-y plane. (Hint: this will
involve a linear system where a, b, and c are the unknowns.)
(b) How many data points (x, y) should be needed to uniquely determine the
coefficients of an nth degree polynomial anx" +an-1²
-1xn-1+...+ a₁x+ao?
Explain your answer in terms of linear systems.
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