Question: Prove OR disprove: if a cubic polynomial with rational coefficients has a constructible root then all its real roots must be constructible. Useful information Definition

Prove OR disprove: "if a cubic polynomial with rational coefficients has a constructible root then all its real roots must be constructible."

Useful information

Definition 12.2.1. A real number is constructible if the point corresponding to it on the number line can be obtained from the marked points 0 and 1 by performing a finite sequence of geometric constructions in the plane using only a straightedge and compass.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

P22-42. Developing a Master Budget for a Manufacturing Organization: Challenge Problem Electric Monkey Computer Accessories assembles a computer networking device from kits of imported components....

ABC reports annual sales of $ 5 million, annual cost of goods sold of $ 2 million, inventory of $ 0.5 million, and net income of $ 0.75 million. What is ABC's annual inventory turns ? Show all...

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

Describe how to construct the function cpo ((D E), v) of two cpos (D, vD) and (E, vE). Prove that ((D E), v) is a cpo. (You may use facts about least upper bounds provided you state them clearly.)...

provide full solution with the given theorems a) Formalizing proof of Theorem 12.3.12. First use the language of 'definition by recursion' to formalize the Definition 12.2.1 for what it means by a...

In Algebra 2, you learned several different methods for solving quadratic equations. For example, you could try factoring, completing the square, or just use the quadratic formula since it ALWAYS...

Activity #1: Root Finding You are to write a program that will find a root of a cubic polynomial. A cubic polynomial is of the form: f(x) = Ax3 + Bx2 + Cx + D Background. All polynomials have some...

Your browser does not have JavaScript enabled. All Apex Learning products require JavaScript. 3.6.6 Test (TS): Polynomial and Rational Functions Test Precalculus Sem 1 (S4201737) Points possible: 100...

All the information are in it (i) g(x) = x?(x + 5)%(x 1)(x 4) (a) Degree: ; Leading coefficient: ; based on this the end behavior is: (b) the x-intercepts: X-intercept Multiplicity Bounce or cross?...

Claire is planning a fashion show and needs to ensure she cannot start preparing the models until she starts arranging the outfits. Which type of dependency is this? Question 7 options:...

1. Use synthetic division to find p(3) for p(x)=x^4-6x^3-4x^2-6x-2 2. what are the real zeros of y=(x-20)^2+5 3. A cubic polynomial with rational coefficients has the roots 6+/-root6 and2/3. Find...

An infestation of a certain species of caterpillar called the spruce budworm can cause extensive damage to the timberlands of the northern United States. It is known that an outbreak of this type of...

Perfect Pet Collar Company makes custom leather pet collars. The company expects each collar to require 2.10 feet of leather and predicts leather will cost $3.70 per foot. Suppose Perfect Pet made 60...

Question 5 0 In organizational structure, _ _ _ _ _ _ refers to how many layers there are in the organization from the top to the bottom.A . horizontal differentiationB. complexityC. vertical...

Ogilvy Company manufactures and sells one product. The following information pertains to each of the company's first three years of operations: Variable cost per unit: Direct materials...

A project has estimated annual net cash flows of $70,000 for four years and is estimated to cost $190,000. Assume a minimum acceptable rate of return of 10%. Using Exhibit 5, determine (a) The net...

Meals on Wheels (MOW) operates a meal home-delivery service. It has agreements with 20 restaurants to pick up and deliver meals to customers who phone or fax orders to MOW. MOW allocates variable and...

Zion Manufacturing had always made its components in-house. However, Bryce Component Works had recently offered to supply one component, K2, at a price of $25 each. Zion uses 10,000 units of...

The financial statements at the end of Paradise Realty's first month of operations are shown below. PARADISE REALTY Statement of Cash Flows For the Month Ended November 30, 20Y3 Instructions 1. Would...

ANSWER , h What I Can Do A. Directions: Write two sentences for each function of communication. 1. Regulation / Control a. b, 2. Social Interaction a. 13; 3. Motivation a. b. 4. Information a. b. 5....

Let F be normal over K and E an intermediate field. Then E is normal over K if and only if E is stable [see Exercise 17]. Furthermore Aut K F/E' Aut K E. Data from exercise 17 If an intermediate...

An integral domain R is a unique factorization domain if and only if every nonzero prime ideal in R contains a nonzero principal ideal that is prime.

Let S be a multiplicative subset of a commutative ring R with identity and let T be a multiplicative subset of the ring s -1 R. Let S * = {r R| r/ s T for some s S}. Then S * is a multiplicative...

The Bendbo Corporation has a total of 300 employees in its two manufacturing locations and the headquarters office. A study conducted five years ago showed the average commuting distance to work for...

Covercraft manufactures covers to protect automobile interiors and finishes. Its Block-It 200 Series fabric has a limited two-year warranty. Periodic testing is done to determine if the warranty...

The data file Trucks contains data on a sample of 200 trucks that were weighed on two scales. The WIM (weigh-in-motion) scale weighs the trucks as they drive down the highway. The POE scale weighs...