Roots Definition and 962 Threads

Homework Statement Find the number and position of real roots of x4+4x3-4x-13=0. Homework Equations The Attempt at a Solution I found the number of real roots using the Descarte's rule of signs. One is positive and other is negative. Now about the position of roots, i don't have...

I'm trying to calculate the cube root of -8, for example, so I type in these buttons: 8 CHS (change sign) Enter 3 1/x y^x But it gives me an error. What is the correct way to go about doing this?

Homework Statement Consider X^4 + 1 in the field \mathbb{Q} [X] . I used Kronecker's theorem to find a root for X^4 + 1 in the field extension \mathbb{Q} [\frac{(1+i)}{\sqrt{2}}] . I'm asked to show that this field extension allows X^4 + 1 to be factorised completely, thus adding a single...

How would I go about approaching this problem? Given the polynomial: x^100 - 3x + 2 = 0 Find the sum 1 + x + x^2 + ... + x^99 for each possible value of x.

[FONT=Times New Roman]Let a,b,c,d be real numbers. Sauppose that all the roots of the equation $z^4 + az^3 + bz^2 + cz + d = 0$ are complex numbers lying on the circle $\mid z\mid = 1$ in the complex plane. The sum of the reciprocals of the roots is necessarily: options a) a b) b c) -c d)...

Hi everyone, I have a question on the discrete Fourier transform. I already know its a change of basis operator on C^N between the usual orthonormal basis and the "Fourier" basis, which are vectors consisting of powers of the N roots of unity. But if i recall correctly from complex...

Homework Statement Find the 6th complex roots of √3 + i. Homework Equations z^6=2(cos(π/6)+isin(π/6)) r^6=2, r=2^1/6 6θ=π/6+2kπ, θ=π/36+kπ/3 The Attempt at a Solution When k=0, z = 2^1/6(cos(π/36)+isin(π/36)), When k=1, z = 2^1/6(cos(13π/36)+isin(13π/36)), When k=2, z =...

Consider field extensions of the form Q(u) where Q is the field of rational numbers and u=e^{\frac{2\pi i}{n}}, the principal nth root of unity. For what values of n is the Galois group of Q(u) over Q cyclic? It seems to at least hold when n is prime or twice an odd prime, but what else...

Homework Statement (a) Find the 6th complex roots of √3 + i. (b) Let A={z|z^6 =√3+i} and B={z|Im(z)>0} and C={z|Re(z)>0}. Find A ∩ B ∩ C. Homework Equations z^6=2(cos(π/6)+isin(π/6)) r^6=2, r=2^1/6 6θ=π/6+2kπ, θ=π/36+kπ/3 The Attempt at a Solution I've done part (a): When k=0, z =...

Hi, I know what roots are and how to find them but I don’t know why they are so important. What is that makes the points where a function become zero so important? I saw a similar post on this topic, but it talks about roots from an optimization point of view. However, finding roots...

Homework Statement Prove that a rational root of a monic polynomial is an integer. Use this to prove that the \sqrt{2} is irrational. Homework Equations The Attempt at a Solution /// I am really not sure where to begin?

rayman's question from another place: Descartes rule of signs tells you this has exactly 1 positive root, and exactly 1 negative root, so it has two real roots. CB

Is it possible to have a cubic polynomial (ax^3+bx^2+cx+d) which has three REAL roots, with one of them being +/- infinity? If there is, can you give an example? Thanks!

I'm sorry, I just realized I put this in the wrong subsection. While I figure out how to fix that, please have a look anyway. __ Homework Statement Given x \inℝ And s =\frac{4(x^{2}) + 3}{2x-1} Prove that s^{2} -4s - 12 ≥ 0 Homework Equations The discriminant Δ, (in order for which to be...

OKAY I have a trg test make up and due tomroow and I have no clue what I am doing, I've searched online chatrooms and they all want money. so this is basiaclly my last hope the test is over rATIONAL ROOTS ZEROS POLYNOMIALS ETC. please show all work if answering QUESTIONS i NEED HELP ON BELOW...

Homework Statement find the sixth roots of i. Homework Equations The Attempt at a Solution So I started by Arg(z)=pi/2 and |z|=1=r n=6 so z= r^(1/6)*e^i((5kpi)/12) for k=0,1,2...n-1 and that's as far as I got and there answer = e^i*n*pi/12 for n=...

Homework Statement Given the fact that z is one of the n-th roots of unity, find the sum below: 1 + 2z + 3z2 + ... + nzn-1Homework Equations (1-x)(1+x+...+xn-1) = 1 - xn The Attempt at a Solution honestly I don't know how to do this. any help is appreciated

Homework Statement http://i.minus.com/i61zvy2BbtqkI.png Homework Equations One can factor the polynomial to (x-1)^2 The Attempt at a Solution After factoring the polynomial, I integrate (x-1) given the bounds of 0 and 1. I get -1/2. The solution manual says the answer is...

Solve the Equation... getting rid of square roots PLZ 1+ √((1+x)√(x^2-24)) = x (x*√(x^2-24)) = (x-1)^2 (Square both side) (-1)+1+(x^√(x^2-24) = (x^2 - 2x +1)-1 x^2(x^2-24) = (x^2 -2x)^2 (Square both sides) x^4 -24x^2 = (x^2 - 2x)^2 x^4 -24x = x^4 - 4x^3 +4x^2 0 = -4x^3 +4x^2 +4x^2 0 =...

Homework Statement I read that if f'(x) is zero once in [a b] then f(x) has maximum two real roots. Why maximum? Shouldn't it be exactly 2? Or it has something to do with the case of repeated roots? Homework Equations The Attempt at a Solution was thinking as in figure

I semi understand the reduction of order method, and i understand the general solution for a 2nd order with repeated roots. however, i can't seem to form up the correct thing to solve this question, and research again proves futile. Any assistance will be appreciated. Use the method of...

I want to prove x^3 + a^2x + b^2 = 0 has one negative and two imaginary roots if b \not= 0. I know that it cannot have any positive real roots because a > 0 and b > 0 will always be the case. I believe I can prove this using Descarte's Rule of Signs (which is in the same chapter of this...

If F is a field of characteristic p, with prime subfield K = GF(p) and u in F is a root of f(x) (over K), then u^p is a root of f(x). Now, I know that x^p \equiv x (\text{mod } p), so isn't it immediately true that f(x^p)=f(x) (over K)? So, 0=f(u)=f(u^p) . I only ask because this type...

1. The problem: Find the value of \lambda for which the sum of squares of the roots of the equation: 2x^2 + (2\lambda +4)x^2-(1+ \lambda) = 0 has minimum value. 2. Homework Equations \alpha + \beta = -b/a \alpha\beta = c/a where a,b,c are coefficients of x^2 , x and constant...

Hello! I am trying to understand this subject but its not simple.. I will ask some question but if anybody wants to write a short introduction which explains my confusions in a continiuous text, that would be awesome as well. :) I think I got a good view of what our weigts are.. just...

can you look this question and help me? http://img252.imageshack.us/img252/2720/59248444.png

Consider a polynomial of the following type: A_n w^n + A_{n-1} w^{n-1}k + A_{n-2} w^{n-2} k^2 + ... + A_1 k^n =0 What are the general conditions on {A_i} in order for the roots w(k) to be EITHER real OR functions with even imaginary parts, Im[w[k]]=Im[w[-k]]? I would be interested in...

Hey everyone! Here I have a problem I don't know how to solve so help would be greatly appreciated! Homework Statement Here is an equation z^3+az^2+bz+c where a, b and c are real numbers. If the roots are drawn in the complex plane they form a triangle with area of 9 units. One root of the...

Help solving a second order ODE with repeated roots, urgent! I have a differential equaition d2y/dx2 - 6dy/dx + 9y = 0 I have found the general solution to be y = (Ax + B)e3x Now I need to find the solutions to A and B so that... when y = 4, x = 0 when y = 49.e15, x = 5 I...

Homework Statement solve the limit: \lim_{x\rightarrow1}\frac{sin(x-1)}{\sqrt{x}-1} The Attempt at a Solution Is there a way of how i can solve this without using l'hospital's rule or taylor series?

Homework Statement Hello there! I'm trying to find the roots of the following cubic polynomial x^3 - 10x + 18 = 0 The Attempt at a Solution I did the following: I rewrite 18 as 18 = - (x^3 - 10x) then I did back substitution and factored out x^3 - 10x - x^3 + 10x = 0 or x(x^2-10) -...

Homework Statement Hello everyone. My task is to find the largest positive root in a specific interval of a function using the bisection method, Newton-Raphson method, and secant method. I've written code for all three of these methods, but the only way I can find all of the roots is to hard...

Homework Statement Hello everyone. My task is to find the largest positive root in a specific interval of a function using the bisection method, Newton-Raphson method, and secant method. I've written code for all three of these methods, but the only way I can find all of the roots is to hard...

Hey everyone! I would really appreciate some help with this problem. I have been racking my brain for hours now, and nothing seems to work/convince me. Homework Statement Show that Un \subseteq U2n for every positive integer, n. Homework Equations [1] Un = {z ε ℂ, zn = 1} [2] Un =...

"roots" command in MATLAB Hey everyone. I'm a new user to Matlab. I must say, it's an awesome program, but not user-friendly at all. I'm having trouble trying to use the "roots" functon. Here's what part b of my problem states: "Use the roots function to compute the time when the aircraft...

Homework Statement Find all solutions to (z2+1)2=-1 The Attempt at a Solution I know that because it is a polynomial of degree 4 it is a square inscribed inside of a circle in the complex plane. All i really need is one solution and from that finding the other three is easy. I have tried...

Homework Statement SOLVE: √(X)-3√(X-1)=1 //That is SQRT(X)-CBRT(X-1)=1; where SQRT = Square root, and CBRT = Cube root. Homework Equations None that I know of... The Attempt at a Solution (I would like to note I have no idea whether I am even approaching this problem the...

Show that the four of the five roots of ... Homework Statement Show that four of the five roots of z5 + 15z + 1 = 0 belong to the annulus {z: 3/2 < |z| < 2}. Homework Equations Argument Principle (presumably) The Attempt at a Solution Since f(z) = z5 + 15z + 1 is entire, it has...

Homework Statement Determine the only real values a, b, c, and d such that the equation: z4+az3+bz2+cz+d = 0 has both z1 and z2 as roots. z1 = 3 + j z2 = -5 + 5j Homework Equations z = x + yj. z = |z|ej\theta The Attempt at a Solution I am not sure where to begin. I can...

Homework Statement Find the quadratic function which has x-intercepts -2 and 2 and passes through the point (0,8). I am struggling with solving this one. I tried to substitute values into ax^2+bx+c=y but there are too many unknowns. Can anyone give some tips how to solve it?

Homework Statement First find all rational zeros of f, then use the depressed equation to find all roots of the equation f(x) = 0. f(x) = x^3 + 5x^2 - 8x + 2Homework Equations The Attempt at a Solution Possible rational zeros: 2, -2, 1, -1 Synthetic division: 1 | 1 5 -8 2 _____1 6 -2...

Hello all, Say one wants to find the inverse Laplace Transform of a function, and the method for attaining the solution is executed via partial fractions. Do the real numbers go with the complex numbers when determining the constants of partials? Perhaps this is wordy. I'll provide a theoretical...

Homework Statement Homework Equations Sum of roots taken one at a time is -b/a Sum of roots taken two at a time is c/a three at a time is -d/a four at a time is e/a The Attempt at a Solution I did part one by solving the two equations...

Homework Statement Show that primitive n-th roots of unity have the form e^{i2\pi k/n} for k\in\mathbb{Z},n\in\mathbb{N}, k and n coprime. The attempt at a solution So the n-th roots of unity z have the property z^{n}=1. I have previously shown that (e^{2\pi ik/n})^{n}=e^{2\pi ik}=(e^{2\pi...

I noticed that 2 grows by 2 when it is squared, and 3 grows by 6 when it is squared, and 4 grows by 12, and 5 grows by 20... etc. etc. So 3's increase when squared is 4 more than 2's increase when squared, and 4's increase when squared is 6 greater than 3's increase when squared, and 5's...

Homework Statement Suppose z is a nonzero complex number z=re^{i\theta} . Show that z has exactly n distinct complex n-th roots given by r^{(1/n)}e^{i(2\pi k+\theta)/n} for 0\leq k\leq n-1. The Attempt at a Solution My attempt: z^{n}=(r\cos\theta+i\sin\theta)^{n}=r^{m}(\cos...

Homework Statement I have a polynimal equation as this - 0.00000000000049125*T^4 + 0.00000000021358333333333333333333333333333*T^3 + 0.00000290233125*T^2 - 0.032444109375*T + 19.891472013020833333333333333333 Homework Equations The Attempt at a Solution I insert those...

Happy new year from France. I am reading books on elementary particle and i see that their gauge bosons may be neutral or have opposite charge. They live in semisimple Lie algebras. So I searched in math books how to prove that in a semisimple Lie algebra if α is a root so is -α. I found...

Need help with this please: Homework Statement (1 + cosθ + isinθ) / (1 - cosθ - isinθ) = icotθ/2 The first step in the solutions shows: (2cos^2θ/2 + i2sinθ/2cosθ/2) / (2sin^2θ/2 - i2sinθ/2cosθ/2) Homework Equations I can't get there. The Attempt at a Solution I tried multiplying by: (1 -...

Homework Statement Let L be a simple compact Lie group, and \Delta_+ is the set of positive roots. I have previously shown that if \alpha\in\Delta_+ and \alpha_i is a simple root, then s_i\alpha\in \Delta_+ where s_i is the Weyl reflection associated with \alpha_i. Now, let \delta =...