Stitz-Zeager_College_Algebra_e-book

# This division shows 1 is a zero descartes rule of

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: on 3.2, we found that we can use synthetic division to determine if a given real number is a zero of a polynomial function. This section presents results which will help us determine good candidates to test using synthetic division. There are two approaches to the topic of ﬁnding the real zeros of a polynomial. The ﬁrst approach (which is gaining popularity) is to use a little bit of mathematics followed by a good use of technology like graphing calculators. The second approach (for purists) makes good use of mathematical machinery (theorems) only. For completeness, we include the two approaches but in separate subsections.1 Both approaches beneﬁt from the following two theorems, the ﬁrst of which is due to the famous mathematician Augustin Cauchy. It gives us an interval on which all of the real zeros of a polynomial can be found. Theorem 3.8. Cauchy’s Bound: Suppose f (x) = an xn +an−1 xn−1 +. . .+a1 x+a0 is a polynomial a0 a1 of degree n with n ≥ 1. Let M be the largest of the numbers: ||an|| , ||an|| , . . . , |a|n−|1 | . Then all the an real zeros of f lie in in the inte...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online
The text provided is an excerpt from a college algebra e-book, discussing methods for finding the real zeros of a polynomial, including the use of synthetic division and theorems such as Cauchy's Bound.
no_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Stitz-Zeager_College_Algebra_e-book

# This division shows 1 is a zero descartes rule of

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: on 3.2, we found that we can use synthetic division to determine if a given real number is a zero of a polynomial function. This section presents results which will help us determine good candidates to test using synthetic division. There are two approaches to the topic of ﬁnding the real zeros of a polynomial. The ﬁrst approach (which is gaining popularity) is to use a little bit of mathematics followed by a good use of technology like graphing calculators. The second approach (for purists) makes good use of mathematical machinery (theorems) only. For completeness, we include the two approaches but in separate subsections.1 Both approaches beneﬁt from the following two theorems, the ﬁrst of which is due to the famous mathematician Augustin Cauchy. It gives us an interval on which all of the real zeros of a polynomial can be found. Theorem 3.8. Cauchy’s Bound: Suppose f (x) = an xn +an−1 xn−1 +. . .+a1 x+a0 is a polynomial a0 a1 of degree n with n ≥ 1. Let M be the largest of the numbers: ||an|| , ||an|| , . . . , |a|n−|1 | . Then all the an real zeros of f lie in in the inte...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online
user
The text provided is an excerpt from a college algebra e-book, discussing methods for finding the real zeros of a polynomial, including the use of synthetic division and theorems such as Cauchy's Bound.

TYPE: NO_QUESTION