Proof that If char K 2,3 then the discriminant of x 3 + bx 2 +cx+
Question:
Proof that If char K ≠ 2,3 then the discriminant of x3 + bx2 +cx+ d is -4c3 - 27d2 + b2(c2 - 4bd) + 18bcd.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 62% (8 reviews)
To prove this we need to first express the discriminant of the cubic polynomial x3 bx2 cx d in terms of its coefficients Recall that the discriminant ...View the full answer
Answered By
Rodrigo Louie Rey
I started tutoring in college and have been doing it for about eight years now. I enjoy it because I love to help others learn and expand their understanding of the world. I thoroughly enjoy the "ah-ha" moments that my students have. Interests I enjoy hiking, kayaking, and spending time with my family and friends. Ideal Study Location I prefer to tutor in a quiet place so that my students can focus on what they are learning.
5.00+
1+ 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
-
Consider f(x) = Ax3 + Bx2 + Cx + D with A > 0. Show that f has one local maximum and one local minimum if and only if B2 - 3AC > 0.
-
The personnel director of a firm has developed two tests to help determine whether potential employees would perform successfully in a particular position. To help estimate the usefulness of the...
-
Modesto Trading Berhad has recently appointed Messrs. Suresh Kumar & Co., Chartered Accountants, to audit the companys financial statements for the year ended 30 June 2021. You are assigned by...
-
You are analyzing the dividend policy of Black and Decker, a manufacturer of tools and appliances. The following table summarizes the dividend payout ratios, yields, and expected growth rates of...
-
How do affirmative action and equal employment opportunity laws differ?
-
Refer to Exercise 9.42 (p. 503). in which managerial success, y, was modeled as a function of the number of contacts a manager makes with people outside his or her : work unit, x, during a specific...
-
The following is the post-closing trial balance for the Whitlow Manufacturing Corporation as of December 31, 2010. The following transactions occurred during January 2011: Jan.1 Sold merchandise for...
-
The given project has an installed cost of $20,000, The annual cost, A=$500 for theforever, and the interest rate i=8% per Year. In addition, it is exnected to be a recurring maior upgrade cost of...
-
Maverick Ltd is a supplier of leisure boats both to the retail trade and to the public. On Monday, Cruise Ltd, one of Maverick Ltd's regular suppliers, agreed to supply Maverick Ltd with 15 carbon...
-
Proof that If F is a splitting field over K of S, then F is also a splitting field over K of the set T of all irreducible factors of polynomials in S.
-
Let / g K(x) with / g K and ,g relatively prime in K[x] and consider the extension of K by K(x). (a) x is algebraic over K(/g) and [K(x): K(/g)] = max (deg ,deg g). (b) If E K is an intermediate...
-
The National Oceanic and Atmospheric Administration publishes temperature information of cities around the world in Climates of the World. A random sample of 50 cities gave the data on average high...
-
According to a recent study, 21% of American college students graduate with no student loan debt. Suppose we obtain a random sample of 106 American college students and record whether or not they...
-
Differentiate the following with respect to x: a. y=5x+2x + x + 15 b. y=4x+3x - 4x - 10 c. y = 3Sin(5x) d. y = 3Cos(3x) e. y=10e -25x f. y = log(6x)
-
Question 2. The rate of drug destruction by the kidneys is proportional to the amount of the drug in the body. The constant of proportionality is denoted by K. At time t the quantity of the drug in...
-
5. 6. -1 (4a) U u X2 1 X2 -2 x -1 -2 12 (4b) U -2 2 Y y 16 x2 X2 3 1 (4c) U u - x 2 Y y -8 Y y -20 5 x X2 2 Find the state space models of the three systems shown in Fig. 4a, Fig. 4b, and Fig. 4c,...
-
Given the following data for Mehring Company, compute total manufacturing costs, prepare a cost of goods manufactured statement, and compute cost of goods sold. Direct materials used $230,000...
-
Refer to the North Valley Real Estate data, which report information on homes sold in the area last year. a. Create a probability distribution for the number of bedrooms. Compute the mean and the...
-
Open Text Corporation provides a suite of business information software products. Exhibit 10-9 contains Note 10 from the companys 2013 annual report detailing long-term debt. Required: a. Open Text...
-
Suppose a participant had a 1999 serum-lutein level of 5.0 μg/dL. What is that persons predicted serum lutein based on the 2003 assay? What is a 95% confidence interval around this...
-
If a serum-lutein value >5.0 g/dL indicates that a participant is taking lutein capsules, then what percentage of the active group is complying? (Assume the old assay is correct and that the serum...
-
If a serum-lutein value <5.0 g/dL indicates that a participant is not taking lutein capsules, then what percentage of the placebo group is complying (not taking lutein capsules outside the study)?...
-
Jennifer purchased a home for $1,000,000 in 2016. She paid $200,000 cash and borrowed the remaining $800,000. This is Jennifer's only residence. Assume that in year 2024, when the home had...
-
business plan describing company with strengths and weaknesses. Any gaps in plan. Recommendations for improvement of the plan.
-
You wish to buy a car today for $35,000. You plan to put 10% down and finance the rest at 5.20% p.a. for six years. You will make equal monthly payments of $_______.
Study smarter with the SolutionInn App