Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![The text discusses the concept of a "double zero" for a polynomial. It states:
The number \( a \) is called a double zero (or a zero of multiplicity 2) of the polynomial \( P \) if
\[ P(x) = (x - a)^2 q(x) \]
and
\[ q(a) \neq 0. \]
The next part asks for a proof:
Prove that if \( a \) is a double zero of \( P \), then \( a \) is a zero of both \( P \) and \( P' \), and \( P''(a) \neq 0 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5936ff2-300d-435d-83da-c517ddce4903%2Fd2425d8d-a93c-414f-8e01-7551ec148bb3%2F8rfvwg_processed.png&w=3840&q=75)
Transcribed Image Text:The text discusses the concept of a "double zero" for a polynomial. It states:
The number \( a \) is called a double zero (or a zero of multiplicity 2) of the polynomial \( P \) if
\[ P(x) = (x - a)^2 q(x) \]
and
\[ q(a) \neq 0. \]
The next part asks for a proof:
Prove that if \( a \) is a double zero of \( P \), then \( a \) is a zero of both \( P \) and \( P' \), and \( P''(a) \neq 0 \).
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