The cubic equation x 3 + ax 2 + bx + a = 0 has roots ,
Question:
The cubic equation x3 + ax2 + bx + a = 0 has roots α, β, γ, and the constants a, b are real and positive.
a. Find, in terms of a and b, the values of Σα and Σ1/α.
b. Given that Σα = Σ1/α, does this cubic equation have complex roots? Give a reason for your answer.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 60% (5 reviews)
a The cubic equation x3 ax2 bx a 0 can be factored as xxx 0 where are the roots of t...View the full answer
Answered By
BillClinton Muguai
I have been a tutor for the past 5 years. I have experience working with students in a variety of subject areas, including computer science, math, science, English, and history. I have also worked with students of all ages, from elementary school to college. In addition to my tutoring experience, I have a degree in education from a top university. This has given me a strong foundation in child development and learning theories, which I use to inform my tutoring practices.
I am patient and adaptable, and I work to create a positive and supportive learning environment for my students. I believe that all students have the ability to succeed, and it is my job to help them find and develop their strengths. I am confident in my ability to tutor students and help them achieve their academic goals.
0.00
0 Reviews
10+ Question Solved
Related Book For
Cambridge International AS & A Level Further Mathematics Coursebook
ISBN: 9781108403375
1st Edition
Authors: Lee Mckelvey, Martin Crozier
Question Posted:
Students also viewed these Sciences questions
-
The cubic equation x 3 - x + 4 = 0 has roots , , . Find the cubic equation that has roots 2 , 2 , 2 . Hence, or otherwise, determine the values of S 6 , S 8 and S 10 .
-
The cubic equation x 3 - x + 3 = 0 has roots , , . a. Using the relation S n , = n + n + n , or otherwise, find the value of S 4 . b. By considering S 1 and S 4 , determine the value of 3 ( + ) +...
-
The cubic equation x 3 - x + 7 = 0 has roots , , . Find the values of and 2 .
-
Is land allowed to be depreciated? Why or why not?
-
The following data are based on information from Domestic Affairs. Let x be the average number of employees in a group health insurance plan, and let y be the average administrative cost as a...
-
Early in 2008, Robbinsville Press was organized with authorization to issue 100,000 shares of $100 par value preferred stock and 500,000 shares of $1 par value common stock . Ten thousand shares of...
-
Explain the financial reporting issue that arises when a company enters into foreign currency transactions. Provide examples of various foreign currency transactions and indicate whether each...
-
Hillcrest Corporation's capital structure is as follows: The following additional information is available. (a) On September 1, 2012, Hillcrest sold 74,000 additional shares of common stock. (b) Net...
-
12.Indicate, by clicking on the relevant boxes, whether the following statements are true or false?
-
Net present value , Internal Rate of Return, Sensitivity Analysis. Francesca Freed wants a Burg-N- Fry franchise. The buy-in is $500,000. Burg-N-Fry headquarters tells Francesca that typical annual...
-
The quartic polynomial x 4 + ax 2 + bx + 1 = 0 has roots , , , . Given that S 2 = S -1 , find 33 in terms of a.
-
You are given the quadratic equation px 2 + qx - 16 = 0, which has roots a and ft. Given also that + = -1/2 and = -8, find the values of p and q.
-
In modern integrated gasification combined cycle (IGCC) coal-fed power plants, oxygen is produced via cryogenic separation of air and is fed to the IGCC plant along with coal. The separation of...
-
Explain the top 5 reasons why SCM analytics might fail in your organization? Make your assumptions to answer this question.
-
Today, let's delve into a critical aspect of warehouse management: resourcing a warehouse. Effective resource allocation is essential for optimizing operations and ensuring the smooth functioning of...
-
Create the ATM application that implements the following functions: Deposits to one of the accounts (saving, checking) Wthdraws from one of the accounts (saving, checking) Displays the balances...
-
A hotel offers a room rate that includes breakfast, lunch, and dinner in its restaurant. The hotel offers: b ) American Plan c ) European Plan d ) Modified American Plan a ) Incentive Plan
-
A guest complains that their room and incidental charges are billed together. However, their company should have paid for the guestroom. What could have resolved this problem? b ) Split folios c )...
-
A pinhole camera doesn't have a lens; a small circular hole lets light into the camera, which then exposes the film. For the sharpest image, light from a distant point source makes as small a spot on...
-
The following information is available for Partin Company: Sales $598,000 Sales Returns and Allowances 20,000 Cost of Goods Sold 398,000 Selling Expense 69,000 Administrative Expense 25,000 Interest...
-
Propose a plausible synthesis for each transformation. a. b. c. d. e. f. g. h. i. j. k. l. m. n. o. p. q. r. s. t. u.
-
Propose a structure for ether with molecular formula C 7 H 8 O that exhibits the following 13 C NMR spectrum. Carbon NMR 114.0 129.5, 120,714.0 55.1- 159.71 160 120 140 100 100 Chemical shift (ppm)...
-
Propose a structure for a compound with molecular formula C 8 H 18 O that exhibits the following 1 H NMR and 13 C NMR spectra. Proton NMR 3.0 2.0 Chemical shift (ppm) 4.0 3.5 2.5 1.5 1.0 0.5 Carbon...
-
Removal of HCl from Propylene Recycle: propose an absorber column to remove HCl from the propylene distillate product that you obtained in problem 4 of HW6. The absorber should operate at 10 C and...
-
In class, we argued that to describe a mixture with nc components in VLE, we need 2n, thermodynamic variables: T, P, ne - 1 mole-fractions, {x}, and ne 1 mole-fractions, {y}. Then, using the VLE...
-
1 4 The SL-1 reactor was a direct-cycle, boiling water reactor of 3 megawatts gross thermal power using fuel highly enriched in U-235, clad in aluminum, and moderated/cooled by water. On January 3,...
Study smarter with the SolutionInn App