Let ƒ (x) E R[x]. Suppose that f(a) = 0 and f'(a) = 0, where f'(x) is the derivative o f(x). Show that (x – a)² divides f(x).
Let ƒ (x) E R[x]. Suppose that f(a) = 0 and f'(a) = 0, where f'(x) is the derivative o f(x). Show that (x – a)² divides f(x).
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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![Let ƒ (x) E R[x]. Suppose that f(a) = 0 and f' (a) = 0, where f'(x) is the derivative of
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Transcribed Image Text:Let ƒ (x) E R[x]. Suppose that f(a) = 0 and f' (a) = 0, where f'(x) is the derivative of
f (x). Show that (x – a)? divides f(x).
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