Suppose p(x) is a polynomial of degree n (n ≥ 0), and z; (0 ≤ i ≤n) are a set of distinct. points on the real axis. Is the following relation true? Briefly explain why. p(x) = p[ro] + p[ro, 21] (x − x0) + p[ro, x1, x2] (x − xo)(x − x₁) + ... + p[ro, 1,...,n] (x − xo)(x − x₁)(x - xn-1)
Suppose p(x) is a polynomial of degree n (n ≥ 0), and z; (0 ≤ i ≤n) are a set of distinct. points on the real axis. Is the following relation true? Briefly explain why. p(x) = p[ro] + p[ro, 21] (x − x0) + p[ro, x1, x2] (x − xo)(x − x₁) + ... + p[ro, 1,...,n] (x − xo)(x − x₁)(x - xn-1)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 29E
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![Suppose p(x) is a polynomial of degree n (n>0), and r, (0 ≤ i ≤n) are a set of distinct
points on the real axis. Is the following relation true? Briefly explain why.
p(x) = p[ro] + p[ro, 21] (x − x0) + p[ro, x1, x2] (x − xo)(x − x₁) + ...
+ p[ro, 1,...,n] (x − xo)(x − x₁)(x - xn-1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad0d55fe-d83b-4711-86a1-cee8ecea510f%2F6d27e681-a76c-4c36-91d2-b1c1181ce837%2Fqn4q0bd_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose p(x) is a polynomial of degree n (n>0), and r, (0 ≤ i ≤n) are a set of distinct
points on the real axis. Is the following relation true? Briefly explain why.
p(x) = p[ro] + p[ro, 21] (x − x0) + p[ro, x1, x2] (x − xo)(x − x₁) + ...
+ p[ro, 1,...,n] (x − xo)(x − x₁)(x - xn-1)
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