For this question, f(x) = 4kx 2 + (4k + 2)x + 1, where k is a
Question:
For this question, f(x) = 4kx2 + (4k + 2)x + 1, where k is a real constant.
a. Find the discriminant of f(x) in terms of k.
b. By simplifying your answer to part a or otherwise, prove that f(x) has two distinct real roots for all non-zero values of k.
c. Explain why f(x) cannot have two distinct real roots when k = 0.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (5 reviews)
a To find the discriminant of fx we need to use the quadratic formula The discriminant is given by t...View the full answer
Answered By
Collins Njuguna
I graduated from Maseno University with a Bachelor of Science in Applied Statistics. After graduation, I started tutoring students in mathematics. My experience in mathematics education is extensive and varied. I have taught a wide range of topics, including algebra, geometry, trigonometry, calculus, statistics, probability, and computer science. I have also worked with students of all ages and backgrounds, from elementary school to college.
My teaching method is based on the idea of hands-on learning. I believe that students learn best when they are actively engaged in the learning process, so I focus on giving students the tools they need to explore the material on their own. I also emphasize the importance of practice and review, as these are essential for mastering math concepts.
I have also developed several online and in-person courses on mathematics. My courses are designed to help students learn mathematics in an efficient and comprehensive way, and I use a variety of activities and exercises to ensure that my students are engaged and motivated.
Overall, my passion for mathematics and teaching has allowed me to be a successful tutor and educator in the field. I am confident that my experience will help your students master the mathematics they need to succeed.
0.00
0 Reviews
10+ Question Solved
Related Book For
Edexcel AS And A Level Mathematics Pure Mathematics Year 1/AS
ISBN: 9781292183398
1st Edition
Authors: Greg Attwood
Question Posted:
Students also viewed these Mathematics questions
-
Suppose this year's dividend of company X is $3. The discount rate on X' stock is 7%: a) If dividend growth rate is 3%, what is the price of the company X? b) If the company's dividends are constant,...
-
Wallace and Brace CPA assign a partner to screen and recommend (or decline) potential clients prior to acceptance. Discuss at least 4 specific issues which should have been considered prior to...
-
Suppose that the person with the above utility function is struck by lightning. He survives, except now his utility function is u = 1 log(x1 1) + 2 log(x2 2). Will his consumption decisions change...
-
McIntyre Industries Work in Process Inventory account had a $68,000 beginning balance on May 1 ($40,000 of this related to direct materials used during April, while $28,000 related to conversion...
-
Which of the following industries have low optimal debt levels according to the trade-off theory? Which have high optimal levels of debt? a. Tobacco firms b. Accounting firms c. Mature restaurant...
-
A measurement is only as good as the measuring device used. For example, a dollar bill is about 6 inches long. I could use this to measure the line and probably obtain a value within 2 inches of the...
-
Stockholders' equity information for two independent companies, Monterrey Enterprises, Inc., and Guadalupe Corp., follow. - Monterrey Enterprises, Inc. Monterrey is authorized to issue 60,000 shares...
-
The overhead application rate for a company is $10 per unit, made up of $6 per unit of fixed overhead and $4 per unit of variable over- head. Normal capacity is 10,000 units. In one month there was a...
-
My Personal Mission Statement: To protect health, improve lives, and promote a healthier quality of life. What am I trying to accomplish? To improve the quality of care we provide and influence...
-
"Part 1: The Performance Lawn Equipment database contains data needed to develop a pro forma income statement. Dealers selling PLE products all receive 18% of sales revenue for their part of doing...
-
Find all of the roots of the function r(x) = x 8 17x 4 + 16.
-
A diver launches herself off a springboard. The height of the diver, in metres, above the pool t seconds after launch can be modelled by the following function: h(t) = 5t 10t 2 + 10, t > 0 a. How...
-
You are given the following information about Sasha Company's inventory for the month of April. Instructions (a) Calculate the cost of goods available for sale and the number of units of ending...
-
The Chinese Motor Company The Chinese Motor Company runs a UK branch and a China branch. Both branches run three departments for sales, car servicing and the sale of parts. Advise the management of...
-
The Depreciation Company The directors of the Depreciation Company are deciding on their accounting policy on the depreciation of their non-current assets. They have just purchased some new assets...
-
Attempt a definition of profit. You can use other books. Can all members of the group agree on the definition? Is the definition clear and robust enough to provide a basis for measuring profits in...
-
Do companies have too much freedom to determine the methods and rates of depreciation that they use for their published accounts? Where governments specify methods and rates of depreciation to be...
-
What four factors should the auditor consider in deciding what evidence, if any, needs to be obtained during the period from the interim date to the balance sheet date?
-
Martha Lou owns 100 shares of Blain Corporation common stock. She purchased the stock on July 25, 1986, for $4,000. On May 2 of the current year, she receives a nontaxable distribution of 100 stock...
-
What services are provided by the provincial and territorial governments?
-
The diagram shows the graph of y = p(x) with 5 points labeled. Sketch each of the following graphs, labeling the points corresponding to A, B, C, D and E, and any points of intersection with the...
-
a. On the same set of axes, sketch y = |12 5x| and y = 2x + 3. b. State with a reason whether there are any solutions to the equation |12 5x| = 2x + 3
-
The function f is defined as f: x 4|x + 6| + 1, x . a. Sketch the graph of y = f(x). b. State the range of the function. c. Solve the equation f(x) = -1/2-1 2.x + 1.
-
What is the major difference between a traditional society and a society of organizations? What are the three reasons time is likely the most powerful asset you have? What are the three examples of...
-
Look at the following job requirement for the Oklahoma Bureau of Investigation and the Florida Department of Law Enforcement special agents. Discuss the differences in education between the two...
-
Case brief assignment. The case you must locate and summarize is: R. v. Mohan, [1994] 2 S.C.R. 9 Source: https://scc-csc.lexum.com/scc-csc/scc-csc/en/item/1131/index.do Breakdown of Marks and...
Study smarter with the SolutionInn App