To determine The maximum possible number of positive and negative roots of 9 x 4 − 12 x 3 − 5 x 2 + 12 x − 4 = 0 . Explanation Definition used: Descartes’ Rule of Signs: 1. The number of positive of a polynomial equation f ( x ) = 0 cannot be greater than the number of changes in sign in f ( x ) in moving from one term to the next in f ( x ) . 2. The number of negative cannot be greater than the number of sign changes in f ( − x ) . Calculation: It is given that the polynomial equation is 9 x 4 − 12 x 3 − 5 x 2 + 12 x − 4 = 0 . Move from left to right, obtain the number of sign changes. From 9 x 4 → − 12 x 3 , − 5 x 2 → + 12 x , and + 12 x → − 4 , there are 3 sign changes. Thus, the number of positive roots is 3. Change the function f ( x ) to f ( − x ) as follows

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

Chapter 15.3, Problem 1PE

To determine

The maximum possible number of positive and negative roots of 9x4−12x3−5x2+12x−4=0.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 15.2, Problem 32E

Chapter 15.3, Problem 2PE

Students have asked these similar questions

ma Classes Term. Spring 2025 Title Details Credit Hours CRN Schedule Type Grade Mode Level Date Status Message *MATHEMATICS FOR MANAGEME... MTH 245, 400 4 54835 Online Normal Grading Mode Ecampus Undergradu... 03/21/2025 Registered **Web Registered... *SOIL SCIENCE CSS 205, 400 0 52298 Online Normal Grading Mode Undergraduate 03/21/2025 Waitlisted Waitlist03/21/2025 PLANT PATHOLOGY BOT 451, 400 4 56960 Online Normal Grading Mode Undergraduate 03/21/2025 Registered **Web Registered... Records: 3 Schedule Schedule Details

Here is an augmented matrix for a system of equations (three equations and three variables). Let the variables used be x, y, and z: 1 2 4 6 0 1 -1 3 0 0 1 4 Note: that this matrix is already in row echelon form. Your goal is to use this row echelon form to revert back to the equations that this represents, and then to ultimately solve the system of equations by finding x, y and z. Input your answer as a coordinate point: (x,y,z) with no spaces.

1 3 -4 In the following matrix perform the operation 2R1 + R2 → R2. -2 -1 6 After you have completed this, what numeric value is in the a22 position?

Chapter 15 Solutions

Basic Technical Mathematics

Ch. 15.1 - Use the factor theorem to determine whether t − 2...Ch. 15.1 - Prob. 2PE Ch. 15.1 - Prob. 3PE Ch. 15.1 - Prob. 4PE Ch. 15.1 - Prob. 1E Ch. 15.1 - Prob. 2E Ch. 15.1 - In Exercises 1–4, make the given changes in the...Ch. 15.1 - Prob. 4E Ch. 15.1 - Prob. 5E Ch. 15.1 - Prob. 6E

Ch. 15.1 - Prob. 7E Ch. 15.1 - Prob. 8E Ch. 15.1 - Prob. 9E Ch. 15.1 - Prob. 10E Ch. 15.1 - Prob. 11E Ch. 15.1 - Prob. 12E Ch. 15.1 - Prob. 13E Ch. 15.1 - Prob. 14E Ch. 15.1 - Prob. 15E Ch. 15.1 - Prob. 16E Ch. 15.1 - Prob. 17E Ch. 15.1 - Prob. 18E Ch. 15.1 - Prob. 19E Ch. 15.1 - Prob. 20E Ch. 15.1 - Prob. 21E Ch. 15.1 - Prob. 22E Ch. 15.1 - Prob. 23E Ch. 15.1 - Prob. 24E Ch. 15.1 - Prob. 25E Ch. 15.1 - Prob. 26E Ch. 15.1 - Prob. 27E Ch. 15.1 - Prob. 28E Ch. 15.1 - Prob. 29E Ch. 15.1 - Prob. 30E Ch. 15.1 - Prob. 31E Ch. 15.1 - Prob. 32E Ch. 15.1 - Prob. 33E Ch. 15.1 - Prob. 34E Ch. 15.1 - Prob. 35E Ch. 15.1 - Prob. 36E Ch. 15.1 - Prob. 37E Ch. 15.1 - Prob. 38E Ch. 15.1 - Prob. 39E Ch. 15.1 - Prob. 40E Ch. 15.1 - Prob. 41E Ch. 15.1 - Prob. 42E Ch. 15.1 - Prob. 43E Ch. 15.1 - Prob. 44E Ch. 15.1 - Prob. 45E Ch. 15.1 - Prob. 46E Ch. 15.1 - Prob. 47E Ch. 15.1 - Prob. 48E Ch. 15.1 - Prob. 49E Ch. 15.1 - Prob. 50E Ch. 15.1 - Prob. 51E Ch. 15.1 - Prob. 52E Ch. 15.1 - Prob. 53E Ch. 15.1 - Prob. 54E Ch. 15.1 - Prob. 55E Ch. 15.1 - Prob. 56E Ch. 15.1 - Prob. 57E Ch. 15.1 - Prob. 58E Ch. 15.1 - Prob. 59E Ch. 15.1 - Prob. 60E Ch. 15.2 - Prob. 1PE Ch. 15.2 - Prob. 2PE Ch. 15.2 - Prob. 1E Ch. 15.2 - Prob. 2E Ch. 15.2 - Prob. 3E Ch. 15.2 - Prob. 4E Ch. 15.2 - Prob. 5E Ch. 15.2 - Prob. 6E Ch. 15.2 - Prob. 7E Ch. 15.2 - Prob. 8E Ch. 15.2 - Prob. 9E Ch. 15.2 - Prob. 10E Ch. 15.2 - Prob. 11E Ch. 15.2 - Prob. 12E Ch. 15.2 - Prob. 13E Ch. 15.2 - Prob. 14E Ch. 15.2 - Prob. 15E Ch. 15.2 - Prob. 16E Ch. 15.2 - Prob. 17E Ch. 15.2 - Prob. 18E Ch. 15.2 - Prob. 19E Ch. 15.2 - Prob. 20E Ch. 15.2 - Prob. 21E Ch. 15.2 - Prob. 22E Ch. 15.2 - Prob. 23E Ch. 15.2 - Prob. 24E Ch. 15.2 - Prob. 25E Ch. 15.2 - Prob. 26E Ch. 15.2 - Prob. 27E Ch. 15.2 - Prob. 28E Ch. 15.2 - Prob. 29E Ch. 15.2 - Prob. 30E Ch. 15.2 - Prob. 31E Ch. 15.2 - Prob. 32E Ch. 15.3 - Determine the maximum possible number of positive...Ch. 15.3 - Prob. 2PE Ch. 15.3 - In Exercises 1 and 2, make the given changes in...Ch. 15.3 - Prob. 2E Ch. 15.3 - Prob. 3E Ch. 15.3 - Prob. 4E Ch. 15.3 - Prob. 5E Ch. 15.3 - Prob. 6E Ch. 15.3 - Prob. 7E Ch. 15.3 - Prob. 8E Ch. 15.3 - In Exercises 3–20, solve the given equations...Ch. 15.3 - Prob. 10E Ch. 15.3 - Prob. 11E Ch. 15.3 - Prob. 12E Ch. 15.3 - Prob. 13E Ch. 15.3 - Prob. 14E Ch. 15.3 - Prob. 15E Ch. 15.3 - Prob. 16E Ch. 15.3 - Prob. 17E Ch. 15.3 - Prob. 18E Ch. 15.3 - Prob. 19E Ch. 15.3 - Prob. 20E Ch. 15.3 - Prob. 21E Ch. 15.3 - Prob. 22E Ch. 15.3 - Prob. 23E Ch. 15.3 - Prob. 24E Ch. 15.3 - Prob. 25E Ch. 15.3 - Prob. 26E Ch. 15.3 - Prob. 27E Ch. 15.3 - Prob. 28E Ch. 15.3 - Prob. 29E Ch. 15.3 - Prob. 30E Ch. 15.3 - Prob. 31E Ch. 15.3 - Prob. 32E Ch. 15.3 - Prob. 33E Ch. 15.3 - Prob. 34E Ch. 15.3 - Prob. 35E Ch. 15.3 - Prob. 36E Ch. 15.3 - Prob. 37E Ch. 15.3 - Prob. 38E Ch. 15.3 - Prob. 39E Ch. 15.3 - Prob. 40E Ch. 15.3 - Prob. 41E Ch. 15.3 - Prob. 42E Ch. 15.3 - Prob. 43E Ch. 15.3 - Prob. 44E Ch. 15 - Prob. 1RE Ch. 15 - Prob. 2RE Ch. 15 - Prob. 3RE Ch. 15 - Prob. 4RE Ch. 15 - Prob. 5RE Ch. 15 - Prob. 6RE Ch. 15 - Prob. 7RE Ch. 15 - Prob. 8RE Ch. 15 - Prob. 9RE Ch. 15 - Prob. 10RE Ch. 15 - Prob. 11RE Ch. 15 - Prob. 12RE Ch. 15 - Prob. 13RE Ch. 15 - Prob. 14RE Ch. 15 - Prob. 15RE Ch. 15 - Prob. 16RE Ch. 15 - Prob. 17RE Ch. 15 - Prob. 18RE Ch. 15 - Prob. 19RE Ch. 15 - Prob. 20RE Ch. 15 - Prob. 21RE Ch. 15 - Prob. 22RE Ch. 15 - Prob. 23RE Ch. 15 - Prob. 24RE Ch. 15 - Prob. 25RE Ch. 15 - Prob. 26RE Ch. 15 - Prob. 27RE Ch. 15 - Prob. 28RE Ch. 15 - Prob. 29RE Ch. 15 - Prob. 30RE Ch. 15 - Prob. 31RE Ch. 15 - Prob. 32RE Ch. 15 - Prob. 33RE Ch. 15 - Prob. 34RE Ch. 15 - Prob. 35RE Ch. 15 - Prob. 36RE Ch. 15 - Prob. 37RE Ch. 15 - Prob. 38RE Ch. 15 - Prob. 39RE Ch. 15 - Prob. 40RE Ch. 15 - Prob. 41RE Ch. 15 - Prob. 42RE Ch. 15 - Prob. 43RE Ch. 15 - Prob. 44RE Ch. 15 - Prob. 45RE Ch. 15 - Prob. 46RE Ch. 15 - Prob. 47RE Ch. 15 - Prob. 48RE Ch. 15 - Prob. 49RE Ch. 15 - Prob. 50RE Ch. 15 - Prob. 51RE Ch. 15 - Prob. 52RE Ch. 15 - Prob. 54RE Ch. 15 - Prob. 55RE Ch. 15 - Prob. 56RE Ch. 15 - Prob. 57RE Ch. 15 - Prob. 58RE Ch. 15 - Prob. 59RE Ch. 15 - Prob. 60RE Ch. 15 - Prob. 61RE Ch. 15 - Prob. 62RE Ch. 15 - Prob. 63RE Ch. 15 - Prob. 64RE Ch. 15 - Prob. 65RE Ch. 15 - Prob. 66RE Ch. 15 - Prob. 67RE Ch. 15 - Prob. 68RE Ch. 15 - Prob. 69RE Ch. 15 - Prob. 70RE Ch. 15 - Prob. 71RE Ch. 15 - Prob. 1PT Ch. 15 - Prob. 2PT Ch. 15 - Prob. 3PT Ch. 15 - Prob. 4PT Ch. 15 - Prob. 5PT Ch. 15 - Prob. 6PT Ch. 15 - Prob. 7PT Ch. 15 - Prob. 8PT

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.