Solved: Proof Generalizing the statement in Exercise 39,
Chapter 1, Problem 40(choose chapter or problem)
Proof Generalizing the statement in Exercise 39, if a polynomial function
\(p(x)=a_{0}+a_{1} x+\cdots+a_{n-1} x^{n-1}\)
is zero for more than n - 1 x-values, then
\(a_{0}=a_{1}=\cdots=a_{n-1}=0\).
Use this result to prove that there is at most one polynomial function of degree n - 1 (or less) whose graph passes through n points in the plane with distinct x-coordinates.
Text Transcription:
p(x)=a_0+a_1 x+...+a_n-1 x^n-1
a_0=a_1=...=a_n-1=0.
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