Show that the given number C is algebraic over Q by finding f(x) Q[x]

Question:

Show that the given number α ∈ C is algebraic over Q by finding f(x) ∈ Q[x] such that f(α) = 0.

1 + √2

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

A First Course In Abstract Algebra

ISBN: 9780201763904

7th Edition

Authors: John Fraleigh

See More Books

Question Posted: Jan 09, 2023 01:44 AM

See More Questions

Find the centroid of the region shown, not by integration, but by locating the centroids of the rectangles and triangles (from Exercise 39) and using additivity of moments. 2 2 2
Find the convergence set for We know that (xn / n! converges for all x. Why can we conclude that limn( xn / n! = 0 for all x? r" 2
14. The potential energy of a 1 kg particle free move along the x-axis is given by V(x)= 4. J. The total mechanical of the particle 2 J. Then, the maximum (2006) energy speed (in m/s) is 2) 3/2 3) 2...
You have observed the following returns over time: Assume that the risk-free rate is 6% and the market risk premium is 5%. a. What are the betas of Stocks X and Y? b. What are the required rates of...
Reconsider Prob. 29.2-2. Suppose now that whether or not the stock goes up tomorrow depends upon whether it increased today, yesterday, and the day before yesterday. Can this problem be formulated as...
0.5 kg of air is compressed reversibly and adiabatically from $80 \mathrm{kPa}, 60^{\circ} \mathrm{C}$ to $0.4 \mathrm{MPa}$, and is then expanded at constant pressure to the original volume....
What's the most Interesting use of robotics you found? LO1
(a) Your roommate says, Sales taxes are reported as an expense in the income statement. Do you agree? Explain. (b) Pearls Cafe has cash proceeds from sales of $8,550. This amount includes $550 of...
Assume that the annual interest rate in the U.S. is 1%, while the annual interest rate in South Africa is 5%. According to Interest Rate Parity, what should the forward rate premium or discount of...
Here is a list of words or phrases discussed in this chapter: 1. Corporation 2. Creditor 3. Accounts receivable 4. Partnership 5. Stockholder 6. Common stock 7. Accounts payable 8. Auditors opinion...
Determine whether there exists a finite field having the given number of elements. 4096
Factory labor data for Knox Company is given in BE20-2. During January, time tickets show that the factory labor of $6,000 was used as follows: Job 1 $2,200, Job 2 $1,600, Job 3 $1,400, and general...
Table 4.7 is another table of interaction effects, with five rows and three columns (five levels of factor A and three levels of factor B). Again, we will assume that only some of the effects are...
How could civil engineers contribute to space debris management and cleanup?
In what ways can the principles of resilient infrastructure be applied to design urban systems capable of withstanding natural disasters, and how do these principles contribute to the overall safety...
What are local variables and global variables in Python?
When to use a tuple vs list vs dictionary in Python? Explain some benefits of Python
What is Lambda Functions in Python? How do I modify a string in python?
Two playing cards are dealt to you from a well-shuffled standard deck of 52 cards. If either card is a diamond or if both are diamonds, you win; otherwise, you lose. Determine whether this game...
After Theorem 1.5 we note that multiplying a row by 0 is not allowed because that could change a solution set. Give an example of a system with solution set S0 where after multiplying a row by 0 the...
a. Based on the value of the standardized statistic obtained in the previous question, do you anticipate the p-value to be small? Why or why not? b. Use an appropriate applet to fi nd and report the...
Suppose that you wanted to investigate whether people tend to pick a big number (3 or 4) rather than a small number (1 or 2). a. In this context, define the parameter of interest and assign a symbol...
Suppose that you wanted to investigate whether people tend to pick a big number (3 or 4) rather than a small number (1 or 2). a. Based on the value of the standardized statistic obtained in the...
Read the following and then answer the questions below:September 12: A Brisbane business offers by letter to sell 500 tyres to a New Zealand company. The Brisbane company does not specify a method of...
Fred returns home from work one day to discover his house surrounded by police. His wife is being held hostage and threatened by her captor. Fred pleads with the police to rescue her and offers...
Would like you to revisit one of these. Consideration must be clear and measurable.if you can't measure it then how can you show it has / has not been done?How can you sue someone for breach of...

Show that the given number C is algebraic over Q by finding f(x) Q[x]

Question:

Step by Step Answer:

Let 1 2 Then 1 ...View the full answer

A First Course In Abstract Algebra

Students also viewed these Mathematics questions