Show that if the roots of the polynomial p are all real, then the roots of p' are all real. If, in addition, the roots of p are all simple, then the roots of p' are all simple.
(1) You are having a meeting with the employees of Financial Outsourcing, Inc. During the meeting, you were asked several questions. Give your opinion to the questions. - Why do you think the Federal government adjusts (raises or lowers) the prime interest rate? - What do you think are some of the effects of the adjustmen
Please help with the following: Express 36 as a product of prime numbers.
Prime number factorization Express 45 as a product of prime numbers
When two numbers are prime numbers the least common multiple is a) 1 b) product of the two numbers c) one of the two numbers d) inf
Problem 1: Prove that there are no integers x, y, and z such that x^2 +y^2 + z^2 = 999 Problem 2: Show that square root of 2 cubed is an irrational number. Problem 3: For each of the following pairs a and b, use the division algorithm to find quotient q and remainder r. (a) b=189, a=17
Please see the attached file for the fully formatted problems.
#1: f(x)=(1x^3-18x^2+101x-168)/(1x^3-2x^2-41x+42) Find: All Roots:? All Holes:? All Vertical Asymptotes:? The answer to the 1st question is NOT 8 or -8. #2: f(x)= (-2x^3+37x^2-222x+432)/(1x^3+3x^2-64x-192) I need the roots: (I have two of them (9/2) and (6) but I need the third)? I need to know the hol
Section 4.3 Collect like terms. 4 4 52. 3a - 2a + 2a + a Collect like terms and then arrange in descending order. 3 3 4 66. -1 + 5x - 3 - 7x + x + 5 Classify the polynomial as a monomial, binomial, trinomial, or none o
1- For n belongs to N (set of natural numbers) let B(n) denote the number of digits used in the binary representation of n. For example B(1) = 1; B(2) = 2; B(3) = 2; B(4) = 3: Find a closed formula for B(n) for an arbitrary n belongs to N. 2: Prove that if gcd(a, b) = d then a/d and b/d are relatively prime. 3- Find
Prove that (Fn+1)^2 - Fn Fn+2 = (- 1)^n
Fill in the function table. when f(x) = x^2 , f(x) = 2x - 1 and f(x) = x^2 - 2x + 1 x f(x) -3 -2 -1 2 4
Theory of Numbers (IX) Principle of Mathematical Induction Fibonacci Number Prove that
Suppose that F1 = 1, F2 = 1, F3 =1, F4 = 3, F5 = 5, and in general Fn = Fn-1 + Fn-2 for n ≥ 3 ( Fn is called the nth Fibonacci number.) Prove that F1 + F2 + F3 +...+ Fn = F(n + 2) - 1
Meaning is given to the sum and product of all the natural numbers and then it is shown that: 1+2+3+4+... = -1/12 1*2*3*4*... = sqrt(2*pi)
Theory of Numbers : Principle of Mathematical Induction - Prove that 1^3 + 2^3 + 3^3 + ... + n^3 = (1 + 2 + 3 + ... + n)^2
Prove that 1^3 + 2^3 + 3^3 + ... + n^3 = (1 + 2 + 3 + ... + n)^2
Assume that n is odd and a is a primitive root mod n. Let b be an integer with b ≡ a(mod n) and gcd (b, 2n) =1. Show that b is a primitive root mod 2n.
Show that for every positive integer n, 8n+1 is not prime.
Prove that there are no integers x, y, and z such that x^2 + y^2 + z^2 = 999.
See attached file. This problem is from the Text Book Mathematical Methods in the Physical sciences 2nd Edition by Mary. L. Boas. Chapter 12. Section 5 problem number 6
List all irreducible polynomial of degree 2, 3 and 4 over F22juu2332. Prove your assertion. Please see the attached file for the fully formatted problems.
Let P(z) and Q(z) be complex polynomials of degree m and n respectively, such that Q(z) has distinct roots z1...zn. Assume that n >= m+2 . Prove that P(z1)/Q'(z1) +...+ P(zn)/Q'(zn) (hint: evaluate ∫c P(z)/Q(z) dz for a suitable curve C).
1) How do I show x+1 is primitive? 2) How do I prove x^4+x^3+1 is an irreducible polynomial of degree 4 over Z mod?
17. The first three Legendre polynomials are P0(x) =1 , P1(x) = x and P2(x)=1/2(3x^2-1). If x = cos θ, then P0(cos θ)=1 and P1(cos θ)= cos θ. Show that p2(cos θ)= 1/4(3 cos 2θ +1). Book:- Differential Equations, by Dennis G Zill, page ,number 17.
23 Polynomials Problems : Solving for Roots, Asymptotes, Word Problems, Finding Equations from Roots, Synthetic Division and Function Composition
1. The figure shows the graphs of f(x) = X 3 and g(x) =AX 3.What can you conclude about the value of a? 2. If f(x)= x(x+3)(x-1), use interval notation to give all values of x where f(x)>0. 3. If f(x) =x(x-1)(x-4)2 , use interval notation to give all values of x where f(x)>0. 4. Find the quotient and remainder of f(x) =
I had to prove 4 theorems two of them dealt with Abelian elements, automorphism of R2 under compontentwise addition. I want to keep my original work in tack as possble BUT I would like the follwing corrections made based on the following comments. THESE ARE THE ISSUES THAT NEED TO BE ADDRESSED The paper needs to provide
Bernoulli Polynomials : Contour Integral Definition, Euler Numbers, Fourier Series, Evaluation of Riemann Zeta function for even integers and Stirling Numbers of the Second Kind
Bernoulli Polynomials are defined and then various properties are demonstrated. Key words: 1) Contour Integral Definition 2) Euler Numbers 3) Fourier Series 4) Evaluation of Riemann Zeta function for even integers 5) Stirling Numbers of the Second Kind
Chapter 3.1 Derivatives of Polynomials and Exponential Functions. I don’t understand how to get the answers provided. Please explain this step by step. Differentiate each function. Y = X2 + 4X +3 V(t)=t2 – 1 Z= A + BeY √ (X) 4√(t3) Y10 Answer Y’=3
A geologist you spoke with is concerned about the rate of land erosion around the base of a dam. Another geologist is studying the magma activity within the earth in an area of New Zealand known for its volcanic activity. One of the shortcuts they apply when doing calculations in the field is to use synthetic division. After t
(See attached file for full problem description) The problem is solved by integration and evaluation between the limits and algebraic manipulation