### Proving the fundamental theorem of algebra by using Rouche's theorem.

How do I prove the fundamental theorem of algebra by using Rouche's theorem?

Explore BrainMass

- Anthropology
- Art, Music, and Creative Writing
- Biology
- Business
- Chemistry
- Computer Science
- Drama, Film, and Mass Communication
- Earth Sciences
- Economics
- Education
- Engineering
- English Language and Literature
- Gender Studies
- Health Sciences
- History
- International Development
- Languages
- Law
- Mathematics
- Philosophy
- Physics
- Political Science
- Psychology
- Religious Studies
- Social Work
- Sociology
- Statistics

- Mathematics
- /
- Algebra
- /

How do I prove the fundamental theorem of algebra by using Rouche's theorem?

When the digits of a two digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11. What is the original number?

Is this expression multiplicative? Justify your answer. f(n)=1, n>1. Factor n into a product of primes,n=p1^k1* p2^k2... then set f(n)= (-1)^k1+k2+...+kr.

Simple Prolog: Please, find the assignment in the file attached. If possible, write as much comment as you can - I really need to understand this material. Thank you for your time.

A table is given that contains many of the basic phrases that you come across when working on word problems. For each phrase, an example is given.

How many cubic yards must one have to excavate using the following guidelines: Driveway size 16 X 17 Paver thickness 2 3/8 Sand bedding 400 Lbs Base compacted 6"

Complete the algebra questions in attachment 1. Find the domain of the given function. 2. Reduce the given expression to lowest terms. 3. Find the solution set of the given equation. Match your result to the correct answer below. 4. Convert the given expression into an equivalent expression that has the indicated denominator

1. Find the center of the ellipse given by 64x2 + 4y2 + 128x - 80y +208 = 0 2. Find the radius of the circle defined by x22 + y2 - 6x -16y = 48 3. The distance between the foci of the ellipse defined by 9(x + 6)2 + 25(y - 15)2 = 225 4. What is the coefficient of x3 in the expansion of (2+ x)5

1. The coefficient of x6y4 in the expansion of (2x-y)10 is ? 2. An arithmetic sequence has a=15 and the common difference d=-3/2. Find the value of 10 over Sigma k=5 ak = the kth term of the sequence. 3. Find the 3rd term in the expansion of (x+6)10.

Exponential and factoring questions

Please see the attached file for the fully formatted problems. Let f(x) = sqrt of x, and show that in this case (f(x+h)-f(x))(f(x+h)+f(x))=h. Use this result to give a simplified expression for f(x+h)-f(x)/h. When f(x) = sqrt x what is lim h-->0 f(x+h)-f(x)/h ?

Please see the attached file for the fully formatted problems. 1: Use the Euclidean Algorithm to find the Highest Common Factor of 1176 and 1960. 2: Use the rules of natural deduction to prove ((A --> (B -->C)) -->((A B)--> C)). [12 marks] 3: Use the rules of natural deduction to prove (A (B U C)) ((A B) C) [14 ma

I need to find a formula that, when multiplied, would generate a 400- digit number

Solve for x. 3x^2-5x+3=0 Written out: Three x squared minus five x plus three equals zero.

Please see the attached file for the fully formatted problem(s). Practice Problems Directions: Show work to support your final result. Examples requiring mathematical work to support the result must be included, if final answer is correct but supporting work is missing. Examples that require a graph DO NOT need the gr

Mrs Fields scored a 1360 on the S.A.T.s. In the math section, she scored 260 more than the verbal section. What were her two scores for each section? Write an equation and solve. math:.... verbal:.....

Solve any 6 equations/inequalities by the indicated method. If no method is indicated then you can solve either algebraically or graphically. Solution by graphing requires a sketch of the graph or a written description of the graph and where the solution lies. Solve any 6 equations/inequalities by the indicated method. If

I have a formula, known as the Bass Curve Formula, that I would like rearranged. The formula generates an S curve that initially grows slowly, then accelerates before slowing down and plateauing. (See example) I would like the formula to be rearranged to find a variable (p). Please find the attached file for a detailed e

How do I simplify: [(8x)/(3x-6)]x[(x2-4)/(2x+4)]

Given equation ln(y/x)=x^2y^2 Find dy/dx

Mary is 3 supervisor in a large office. The secretaries are constantly talking to each other. Mary 's concerned that this constant jabbering back and forth is causing low efficiency in T.e office. She decides to separate the secretaries by the greatest possible distance within the confines of the office. Your task is to decide

F(x)=-x^4+12x^3-58x^2+132x The concentration of a drug, f(x), in parts per million, in a patients's blood x hours after the drug is administered is given by the function. I need to make a graph of the following: a) how many hours after the drug is administered will it be eliminated from the patients's bloodstream b) how

I need help on how to solve the value of x for quadrilaterals.

Solve for y. 1) 2/3 -3y +7y = 7/3 +8y 2) 5(y-3) = 3y-4 ------ 4

Solve for x: 1.8^(2x+3) = 0.72^1/3

Please see the attached file for the fully formatted problems. Algebra problems DIRECTIONS: It is a little trickier to do online because of the graphs. For the equations/inequalities that require a graphical solution, you will have to describe what part of your graph provides the answer. If you scan in your work, then in

Solve for x: 6/(x^2-7x+6)=2/(x-1)-4/(x-6)

Factor: -2x^3 - 16x^2 + 40x

Find the fourth term of this expansion: (3x-4y)^11

Show that Log (z) is discontinuous along the negative real axis.