Roots Definition and 978 Threads

Homework Statement Show that p(x) = x^2 - \sqrt2 is irreducible in \mathbb Z[\sqrt 2] . The Attempt at a Solution I think I have this, but I just want to make sure my reasoning is correct. I'm sure there are other ways. Firstly, it is sufficient to show that p(x) is irreducible in the...

I have been seeing a few during in my practice questions which leaves me worrying. If it is a quadratic function, the irrational numbers can be easily obtained using the equation. However, I got a question today which eventually took this form: 28D3+36D2-41D2+4 = 0 (I reevaluated...

Homework Statement Find the general solution to y'''+y=0 Homework Equations The Attempt at a Solution y''+y=0 r^3+1=0 r^3=-1 r=(-1)^(1/3) --------------------- -1=-1+0i -1=cos(pi)+isin(pi)=e^(i*pi) -1=cos(pi+2xpi)+isin(pi+2xpi)=e^i(pi+2xpi) --------------------------...

Hi, I was looking at the derivation of the equation for a hyperbola on Wolfram Mathworld. In one step, the webpage instructs you to "complete the square". It starts with: \sqrt{\left(x -c\right)^{2} +y^{2}}-\sqrt{\left(x+c\right)^{2}+y^{2}} = 2a and then says, "rearranging and completing...

Casus irredicibilis describes a situation where a cubic polynomial with integer coefficients has three distinct real roots, but you can't express those roots using just real numbers and radicals. Instead, if you want to only use radicals, then you must use complex numbers, even though the roots...

Homework Statement if p is a prime of the form p=4k+1 and g is a primitive root of p, show that -g is a primitive root. I'm not sure if this is a decent proof or not. My final argument looks suspicious. Any thoughts? Thanks Tal The Attempt at a Solution First, notive that...

Hi, I'm currently doing a project and this topic has come up. Are there any known famous classes of polynomials (besides cyclotomic polynomials) that fit that description? In particular, I'm more interested in the case where the polynomials have odd degree. I know for example that the roots of...

Homework Statement This isn't really a question on its own, rather a step in the solution to another question: How would I prove that y= A\cos x + B\sin x (A, B arbitrary constants) has at least n zeroes in the interval [\pi , \pi (n+1)] where n\in\mathbb{Z}\;? (I don't need to be too...

i have this function f(x) = (1 − 6x^2)^-1 and I need 21 roots between [-1,1] equidistant (the points to be at same distance from one to another) can i find the roots with some function in matlab? i found out just the polyval function for polynom

Homework Statement Find the roots of y-y^3=1 Homework Equations The Attempt at a Solution Factor theorem doesn't help in this equation. Found from Wikipedia, a very complex formula is needed to solve cubic eq. Can someone show me the steps to find the root? Thank you ^^

Homework Statement Find the zeros of the cubic equation: y = x^3 -9x^2 + 15x + 30 How do we find the zeros of this? In this case, subbing in x-values that will make it equal 0 does not work.

I want to find roots of a function using MATLAB. The function is x*tan(x)-A=0. "A" is an arbitrary constant. If I use fzero or fsolve, it will find the root closest to the guess. Is there any way of getting, say, the first 5 roots of this function? I don't know where the roots are at, so I...

Homework Statement The equation A2/(x-a) + B2/(x-b) + C2/(x-c) + ... + H2/(x-h) = k has 1) No real root 2) At most one real root 3) No complex root 4) At most two complex roots The Attempt at a Solution We can see that the function f(x) = L.H.S. - R.H.S. is a strictly decreasing...

Homework Statement Solve: 2x2y" + xy' - y = 3x4 Homework Equations The Attempt at a Solution I know this is a Euler Cauchy solution because of the x2 before the y" in the ODE. I try to solve the characteristic equation m2 +(a-1)m + b = 0 I get 2m2 + (1-1)m - 1 =0 or 2m2 -...

Homework Statement The sum of the fourth powers of the roots of the equation x3+x+1=0 is? The Attempt at a Solution Is there any shortest method to find out the answer using some formulae? I know a method but its very very lengthy and time consuming.

Homework Statement what happens to the number of solutions of the equation x = \tanh(\beta x) When \beta is varied from \frac{1}{2} to \frac{3}{2} [/tex] a) unchanged b) increase by 1 c) increase by 2 d) increase by 3 Homework Equations...

Homework Statement Perhaps this is trivial, but working in thermodynamics oftenly requires of handling with logarithms. For example, in an exercise I'm trying to solve, I need the roots for something like: x+ln (x)=constant The thing is I don't know how to find this kind of roots. I mean, I...

Homework Statement $ \lim_{x\to0}\frac{\sqrt{x+1} - \sqrt{2x+1}}{\sqrt{3x + 4} - \sqrt{2x+4}} The Attempt at a Solution Ok, I just want to know what is the easiest approach tactic one could take to solve this. I tried doing the conjugate to rationalize the denominator, but then...

Homework Statement lim x -> infinity : sqrt(x^2 + 4x(cos x) ) - x find the limit (or lack there of) Homework Equations look above The Attempt at a Solution ok so i used the addition/subtraction law to show that the limit of f(x) = - x as x --> infinity = infinity now for the other half...

Homework Statement Let f_n(z)=\sum_{k=0}^n\frac{1}{k!}z^n. Show that for sufficiently large n the polynomial f_n(z) has no roots in D_0(100), i.e. the disk of radius 100 centered at 0. Homework Equations This is a sequence of analytic functions which converges uniformly to e^z on C...

Homework Statement I need to find the roots of some functions using the bisection method, secant method, etc in Matlab. I have the m-files written, but I'm having trouble putting the function F(x)=e^{-0.5x}(4-x)-2 into Matlab. I had no problem with F(x)=0.95x^{3}-5.9x^{2}-6 but I don't...

1. Find the cube roots of the complex number 8+8i and plot them on an Argand diagram Thats the problem, I've had a go at the solution and came up with 3 solutions using the \sqrt[n]{r}*(cos(\frac{\theta+2\pi*k}{n})+isin(\frac{\theta+2\pi*k}{n})), but the answers (roots) I get, I can't plot it...

I have some doubts regarding SU(3). These are at very basic level. First, how does one construct adjoint representation of SU(3)? What will be the dimensionality of the matrices? The defining matrices in terms of Gell-Mann matrices are 3x3 but in the case of adjoint representation the matrices...

Homework Statement If equation https://www.physicsforums.com/attachment.php?attachmentid=32867&stc=1&d=1299509982 has n positive roots, then least value of n for which a2 + a3 is negative, is The Attempt at a Solution Time allotted is 1 minute. I have no idea of solving such questions.

Homework Statement I have no problem using DeMoivre's Theorem to find nth roots of a complex number. However, I really don't know what this is accomplishing. Usually the book I use explains the concept behind a certain type of problem, but in this case, there is nothing. I can easily get...

Homework Statement Hi guys, I am having difficulty with the following problem: Show the complex sine function has real valued zeros. Homework Equations I know that sin(z) = (e^iz - e^-iz) /2iThe Attempt at a Solution I have to find roots of sin(z), i.e, when the above equation = 0. First I...

Homework Statement Find the square roots of 8 and 10 in \mathbb{F}_{11}, ie. the integers mod 11. The Attempt at a Solution Well, I ran over all the possibilities, but I can't find it. It has been suggested to me that perhaps you could express it in terms of other square roots somehow, but...

Homework Statement Question: I'm confused about how to app Find the real-valued general solution of the differential equation y''+1y'+1y=0 where primes indicate differentiation with respect to x. (Use the parameters a, b, etc., for undetermined constants in your solution.) The...

how to determine which is the answer to positive sqrt and negative sqrt in this problem? substituting works but what if the equation is very long and you can't use calcu or computers http://i.imgur.com/SkcQZ.png also is there a way to solve this without squaring both sides?

Homework Statement I must show that cos(2pi/n) + isin(2pi/n) is a primitive root of unity Homework Equations a primitive root of unity is an nth root of unity that does not equal 1 when raised to the kth power for k less than n and great than or equal to 1 The Attempt at a Solution...

http://img717.imageshack.us/img717/4...10106at123.png its a construction from felix klein, around 1900. it should be made without trigonometric functions or complex algebra etc. the ratios of lengths should be sufficient, but i have only found one similar triangle and then i got stuck...

Started my first year of Electronic Engineering a few months back and I'm already struggling with the mathematics. I have been to this forum a number of times over the last year and finally decided to join just 10 minutes ago!Homework Statement Find the roots of P(x) given that two roots are...

Im not sure if this should go in the math/number theory section or here, but here it goes: how do programs calculate the primitive roots mod n of extremely large primes? My program will only go up to 12-14 bits before having memory errors caused by storage of the totient of the prime number...

I have read several books on the Riemann Hypothesis and have a general understanding of the non-trivial zeros and their real part 1/2. In my own studies I have devised a root system based upon some of Euclid’s ideas and congruence that identifies some interesting properties of the square roots...

Homework Statement 1)Prove that the characteristic roots of a hermitian matrix are real. 2)prove that the characteristic roots of a skew hermitian matrix are either pure imaginary or equal to zero. Homework Equations The Attempt at a Solution

Show that Q/Z is isomorphic to the multiplicative group U∗ consisting of all roots of unity in C. (That is, U∗ = {z ∈ C|zn= 1 for some n ∈ Z+}.) I don't really understand how to prove this isomorphism

Homework Statement With f(z) = 2z^{4} +2z^{3} +z^{2} +8z +1 Show that f has exactly one zero in the open first quadrant.Homework Equations Argument PrincipleThe Attempt at a Solution I know I'm supposed to use the Argument Principle.. So far, all I can do is show something like, in the unit...

Homework Statement Solve the equation 2cos^2\theta + 5cos\theta - 3 = 0\ for\ \frac{3\pi}{2}<\theta<5\pi Homework Equations quadratic equation, power reduction formula: cos^2\theta = \frac {1+cos2\theta}{2} The Attempt at a Solution First I tried using the quadratic...

Homework Statement The equation: x^3 + ax + b = 0 has 3 roots, u, p and q. Give the general solution for for an equation with roots (u/p)+(p/u), (p/q)+(q/p) and (u/q)+(q/u) Homework Equations u + p + q = 0 upq = -b up + uq + pq = a If you can solve it you probably...

I want to know how to compute the probability that a random quadratic equation of the form a x2+b x+c=0 has real roots. So, i want to find the probability that b2>4ac (assuming each variable has a continuous constant distribution in an interval (-R,R)) I know that the probability is about...

I'm trying to prepare for an exam and we were warned that the Laplace transforms given to us may have Complex roots, double roots, or double complex roots. I'm comfortable with complex roots, but I can't find a problem in the textbook that deals with double roots, and I haven't used them since...

Homework Statement (a) Find a primitive root β of F3[x]/(x^2 + 1). (b) Find the minimal polynomial p(x) of β in F3[x]. (c) Show that F3[x]/(x^2 + 1) is isomorphic to F3[x]/(p(x)). The Attempt at a Solution I am completely lost on this one :confused:

Homework Statement Show that the equation (9x^5)-(4x^4)+(8x^3)-4x+1=0 has exactly 3 real roots. Homework Equations The Attempt at a Solution I found a derivative of (45x^4)-(16x^3)+(24x^2)-4. I am not sure how to set this equal to zero

I need to find the derivative of the square root of (2x+1) (not sure how to do square root symbol here, sorry) I understand that the square root of (2x+1)= (2x+1)^(1/2), but I am getting a little confused on how to continue from there.

If someone could guide me as to how I can approach this that would be appreciated. Suppose f(x) and g(x) have continuous first derivatives on R and that f(x) g'(x) - g(x) f'(x) does not equal 0. Prove that between two consecutive roots of f(x) there is exactly one root of g(x).

I have trouble figuring out this problem. If someone can help me out that would be appreciated. Suppose we have x^3 -x + C let r denote the largest root of the equation. What's a mathematical way of relating r and C? (quantitative). Also what's dr/dc Thanks in advance.

Homework Statement Consider the following equation in y: Ay2 – 3y + 4 = 0. What is the range of possible values for A such that the two roots are both real? Homework Equations The Attempt at a Solution Not sure how to approach this problem.

This is taken from Wikipedia: Many of the methods for calculating square roots of a positive real number S require an initial seed value. If the initial value is too far from the actual square root, the calculation will be slowed down. It is therefore useful to have a rough estimate, which...

Could someone please explain the y2 solution for repeated roots in Frobenius method where y2=y1lnx+xs \Sigma CnxnI am struggling to figure out how to solve this

I'm kind of confused about how to approach a function with the chain rule. For example in the equation ƒ(x) = sqrt(1-sin(x)) I know i simplify it to ƒ(x) = 1-sin(x)^(1/2) but I'm lost from there.