Roots Definition and 978 Threads

Show that the equation x^3-12x-7.2=0 has one positive and two negative roots: I know this can be solved by trial and error, and finding f(0),f(1-4),f(-1 - -4) I have shown that It has two negative roots and one positive however I'm wondering if there is another method on how to show it has...

Ok, to start off I have been examining the structure of polynomials. For instance, consider the general polynomial P(x)=\sum^{n}_{k=0}a_{k}x^{k} (1) Given some polynomial, the coefficients are known. Without the loss of generality...

srirahulan's question titled "Algeb" from Math Help Forum, Hi srirahulan, Let \(\alpha\mbox{ and }\beta\) be the two roots of these quadratic equations. Then, according to the first equation, \[\alpha+\beta=-\frac{2}{a}~~~~~~(1)\] Considering the second equation...

Homework Statement The two polynomial eqns have the same coefficients, if switched order: a_0 x_n+ a_1 x_n-1 + a_2 x_n-2 + … + a_n-2 x_2 + a_n-1 x + a_n = 0 …….(1) a_n x_n+ a_n-1 x_n-1 + a_n-2 x_n-2 + … + a_2 x_2 + a_1 x + a_0 = 0 …….(2) what is the connection between the roots of...

Hi, I am struggling with this puzzle from a book. Puzzle : Can you find a number n such that, the numbers n-7, n, and n+7 have rational square roots (can be expressed as integers or fractions)? According to the book one of the solutions is n =113569 /14400 This is what I have done so...

we are given an equation x5+x=10 . How to prove that the only root for the equation is irrational? I'm an average 12th standard student. So, please keep it low. Thanks in advance.

Homework Statement I'm supposed to find the 6 roots of -8 + 0i we are told the usual method of for these problems is to put the complex number into it's exponential form like so z = |z|exp( i(θ+2πk)) where k: [0 to n-1] then put it to the relevant power 'n' z1/n = |z|1/nexp(( i(θ+2πk)/n)...

Homework Statement Simplify...Homework Equations Starting Equation: ³√9xy^4 * ³√12x³yThe Attempt at a Solution (Sorry ahead of time if this is sloppy) ³√9xy^4 * ³√12x³y - I broke up each part of the cubed roots to try and simplify them³√9 * ³√x * ³√y * ³√y³ * ³√y * ³√12 *...

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.

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) d ---------- Post...

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...

Hi all I found these equalities from Gordon Brown (1963). He uses the killing form to measure the length of the roots in a semi simple algebra. First and second equalities are quite obvious and come from the definition. Could you help me for the last one which prove that we have a...

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...