The polynomial of degree 4, P(x) has a root of multiplicity 2 at a = 2 and roots of multiplicity 1 at a = 0 and a = -2. It goes through the point (5, 157.5). Find a formula for P(x). P(x) =
The polynomial of degree 4, P(x) has a root of multiplicity 2 at a = 2 and roots of multiplicity 1 at a = 0 and a = -2. It goes through the point (5, 157.5). Find a formula for P(x). P(x) =
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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![**Problem Statement:**
The polynomial of degree 4, \( P(x) \), has a root of multiplicity 2 at \( x = 2 \) and roots of multiplicity 1 at \( x = 0 \) and \( x = -2 \). It goes through the point \( (5, 157.5) \).
Find a formula for \( P(x) \).
**Task:**
\[ P(x) = \, \]
*Note: The problem requires finding the polynomial based on the given roots and point. The polynomial can be expressed as a product of linear factors raised to the power of their multiplicities. Substitute the given point to find any unknown coefficient.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F107b68ef-5916-46d8-b604-d8abbf265ef5%2F38c0cd48-a08b-45ab-b5a2-11a855b4ffa6%2F2ug4yz8i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
The polynomial of degree 4, \( P(x) \), has a root of multiplicity 2 at \( x = 2 \) and roots of multiplicity 1 at \( x = 0 \) and \( x = -2 \). It goes through the point \( (5, 157.5) \).
Find a formula for \( P(x) \).
**Task:**
\[ P(x) = \, \]
*Note: The problem requires finding the polynomial based on the given roots and point. The polynomial can be expressed as a product of linear factors raised to the power of their multiplicities. Substitute the given point to find any unknown coefficient.*
Transcribed Image Text:Let \( f(x) = 1(x - 4)(x - 5)^2 \).
Fill out the table below. In the third column, type the word crosses for a zero where the curve crosses through to the other side of the \( x \)-axis, or touches for a zero where the curve approaches the \( x \)-axis, touches it, and reverses direction without crossing over it.
| zero | multiplicity | crosses or touches the \( x \)-axis |
|------|--------------|-------------------------------------|
| | 1 | |
| 5 | 2 | |
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