The cubic equation x 3 - x 2 - 3x - 10 = 0 has roots ,
Question:
The cubic equation x3 - x2 - 3x - 10 = 0 has roots α, β, γ.
i. Let u = -α + β + γ. Show that u + 2α = 1, and hence find a cubic equation having roots -α + β + γ, α -β + y, α + β – γ.
ii. State the value of αβγ and hence find a cubic equation having roots 1/βγ, 1/γα, 1/αβ.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 50% (6 reviews)
Answer i Let u Then we have Now let us divide the equation by u to ...View the full answer
Answered By
Enock Oduor
I am a chemist by profession, i coach high school students with their homework, i also do more research during my free time, i attend educational and science fair seminars where i meet students and do some projects.
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 5x 2 + 1 = 0 has roots , , . a. Find the values of S 1 and S 3 . Another cubic equation has roots 2 , 2 , 2 . b. Find the cubic equation with these roots. c. Hence, or...
-
The cubic equation x 3 + 3x 2 - 1 = 0 has roots , , . Show that the cubic equation with roots + 2/, + 2/, + 2/ is y 3 3y 2 9y + 3 = 0. Hence, determine the values of: a. ( + 2)( + 2)( + 2)/ b. /...
-
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 .
-
Day and Night formed an accounting partnership in 2014. Capital transactions for Day and Night during 2014 are as follows: Partnership net income for the year ended December 31, 2014; is $68,400...
-
Consider the following Minitab display of two data sets: (a) What are the respective means? the respective ranges? (b) Which data set seems more symmetrical? Why? (c) Compare the interquartile ranges...
-
Product pricing and promotion decisions should usually be based on their effect on contribution margin , not on gross margin. Explain how using an absorption costing format for the income statement...
-
Foreign Exchange Market Characteristics. With reference to foreign exchange turnover in 2013, rank the following: a. The relative size of spot, forwards, and swaps b. The five most important...
-
Allison Cooper opened Allisons Toy House. As her newly hired accountant, your tasks are to do the following: 1. Journalize the transactions for the month of October. 2. Record to subsidiary ledgers...
-
(3x^(3)yz^(2)-xy^(4)z^(3)-11x^(2)y^(2)z^(5))-(3x^(2)yz^(3)+15xy^(4)z^(3)-4x^(2)y^(2)z^(5)) difference is implify your answer. Do not factor.
-
There is a lottery with n coupons and n people take part in it. Each person picks exactly one coupon. Coupons are numbered consecutively from 1 to n, n being the maximum ticket number. The winner of...
-
If a + b = -3 and 2 + 2 = 7, find the value of ab and, hence, write down a quadratic equation with roots and .
-
Given that 3x 2 - 2x + 9 = 0 has roots , , find the quadratic equation with roots + 1/, + 1/.
-
Assume your home is assessed at $200,000. You have a $150,000 loan for 30 years at 6 percent. Your property tax rate is 1.5 percent of the assessed value. In year one, you would pay $9,000 in...
-
What is force? What are three laws of Newton? Give one example of each from your life where you may use them?
-
Reflecting specifically on the resources made available this week, which i have included below, please respond to the following: https://youtu.be/DUyzjeOrwnw?si=ccLpGzCF3CRKpekf...
-
Consider an unknown semiconductor. At 270 K, you measure a resistance of 0.01 Ohms, while at a temperature of 300 K, you measure a resistance of 2.591 10-4 Ohms. 1) What is the gap of this material,...
-
Research on physics used in robotics lists 3 types of robots where these robots can be used components of a robot such as power unit and manipulator, sensors, actuators controller, analog sensors vs...
-
Explain at least four causes of organizational conflict. Explain the main barriers to change at the individual level that the internal change agents are likely to encounter as they introduce the new...
-
Improvements in technology usually result in lower costs of production or new and improved consumer goods and services. Assume that an improvement in medical technology results in an increase in life...
-
Maria Castigliani is head of the purchasing department of Ambrosiana Merceti, a medium-sized construction company. One morning she walked into the office and said, The main problem in this office is...
-
Ramelteon is a hypnotic agent used in the treatment of insomnia: a) What is the molecular formula of this compound? b) How many sp 3 -hybridized carbon atoms are present in this structure? c) How...
-
For each compound below, identify the most acidic proton in the compound: (a) (b) (c) (d) (e) (f) (g) (h) -NH2 -
-
The following reaction is observed to be regioselective. Draw a mechanism for the reaction, and explain the source of regioselectivity in this case: Br HE.
-
TB 05-75 2/10,n/30 is interpreted as
-
Kenneth Clark is one of Texas's premiere party planners. She purchases a variety of supplies, such as plastic tableware. stemware, and decorations, throughout the year. Kenneth has prepared the...
-
Problem 3-14 (Algo) Schedule of Cost of Goods Manufactured; Overhead Analysis [LO3-3, LO3-4] Gitano Products operates a job-order costing system and applies overhead cost to jobs on the basis of...
Study smarter with the SolutionInn App