Suppose K is a subfield of R (so that F may be taken to be a subfield
Question:
Suppose K is a subfield of R (so that F may be taken to be a subfield of C) and that /is irreducible of degree 3. Let D be the discriminant off Then (a) D > 0 if and only if /has three real roots. (b) D < 0 if and only if /has precisely one real root.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 57% (7 reviews)
Let fx be an irreducible polynomial of degree 3 over K and let be a root of fx in some ...View the full answer
Answered By
Mary Boke
I have teached the student upto class 12th as well as my fellow mates.I have a good command in engineering,maths and science.I scored 90+ marks in 10th and 12th in maths.
0.00
0 Reviews
10+ Question Solved
Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
Question Posted:
Students also viewed these Mathematics questions
-
Let K := {s + t2 : s; t Q}. Show that K satisfies the following: (a) If x1; x2 K, then x1 + x2 K and x1x2 K. (b) If x 0 and x K, then 1/x K. (Thus the set K is a subfield of R. With the order...
-
Steves employer provides him with several fringe benefits. Which of the following are included in his taxable income? A) Group term life insurance premium paid by employer for $40,000 coverage for...
-
Let M > 0 be a fixed positive definite n n matrix. A nonzero vector v 0 is called a generalized eigenvector of the n n matrix K if Kv = Mv, v 0, (8.31) where the scalar is the corresponding...
-
A ping pong ball is drawn at random from an urn consisting of balls numbered 4 through 9. A player wins $1.5 if the number on the ball is odd and loses $1.5 if the number is even. Let x be the amount...
-
GL Corporation, a retail firm, is making a decision on how much it should pay out to its stockholders. It has $100 million in investible funds. The following information is provided about the firm:...
-
What methods is been used to implement practice-based patient-care learning and quality improvement approaches in integrated care settings for substance use disorder? 2. What specifically can you do...
-
Calculate the speed of sound in air, helium, and hydrogen. The temperature is \(70^{\circ} \mathrm{F}\).
-
The Farmington City Council recently commissioned a study of park users in their community. Data were collected on the age of the person surveyed and the amount of hours he or she spent in the park...
-
Discuss disparities in the sentencing of defendants in our criminal justice system based on wealth. Cite at least one example and a valid external source of information (case, journal article, legal...
-
Sketch a set of equidistant 113 planes in a cubic unit cell.
-
Let L and M be subfields of F and LM their composite. (a) If K L M and M = K(S) for some S M, then LM = L(S). (b) When is it true that LM is the set theoretic union L M? (c) If E 1 , ... , E n...
-
Proof that If u F is purely inseparable over K, then u is purely inseparable over any intermediate field E. Hence if F is purely inseparable over K, then F is purely inseparable over E.
-
Which of the following would be optically active? (a) A pure sample of A (b) A pure sample of B (c) A pure sample of C (d) An equimolar mixture of A and B
-
The following information was obtained from the records of Shae Incorporated: Merchandise inventory $ 1 4 4 , 0 0 0 Notes payable ( long - term ) 1 6 0 , 0 0 0 Net sales 4 8 0 , 0 0 0 Buildings and...
-
Midterm Project: For now, take revenues as fixed. You may not alter the amount of money you have to spend. Assume that you have the exact same amount of money this year, as you did last year...
-
The manager of an absolute return fund most likely aims, over any 12month period, to: Group of answer choices Generate positive returns. Outperform its peer group. Outperform a recognized benchmark...
-
Dot - to dot pictures and coloringbooks are not creative art activities. Explain why they aren'tcreative and describe some art activities that you would consider creative.
-
USA Logistics (a US corporation) is a wholly-owned subsidiary of EuroConnect (a foreign corporation). In the current year, USA Logistics had $99,000,000 of US taxable income (all US source),...
-
People swam across Lake Ontario 52 times between 1974 and 2013 (www.soloswims.com). We might be interested in whether they are getting any I faster or slower. Here are the regression of the crossing...
-
You continue to work in the corporate office for a nationwide convenience store franchise that operates nearly 10,000 stores. The per- store daily customer count (i.e., the mean number of customers...
-
Compare the means of each pair of groups using the Bonferroni method? Pulmonary Disease Twenty-two young asthmatic volunteers were studied to assess the short-term effects of sulfur dioxide (SO 2 )...
-
Is a fixed-effects or a random-effects ANOVA appropriate here? Hypertension Automated blood-pressure measuring devices have appeared in many banks, drugstores, and other public places. A study was...
-
Test whether the mean difference is consistent over all four locations? Hypertension Automated blood-pressure measuring devices have appeared in many banks, drugstores, and other public places. A...
-
Have Canadian social services been protected under NAFTA and, if so, how?
-
What were Theranos' machines supposed to accomplish? Holmes approached a number of pharmaceutical companies to demonstrate her first machine -what was the outcome of these various test? Did Holmes...
-
Beric Dandarrion Company plans to sell 5 0 0 , 0 0 0 units of finished product in January 2 0 1 9 . Beric anticipates a growth rate in sales of 4 % per month thereafter; and, desires a monthly ending...
Study smarter with the SolutionInn App