Root Definition and 918 Threads

Let p be a prime number. Find all roots of x^(p-1) in Z_p I have this definition. Let f(x) be in F[x]. An element c in F is said to be a root of multiplicity m>=1 of f(x) if (x-c)^m|f(x), but (x-c)^(m+1) does not divide f(x). I'm not sure if I use this idea somehow or not.

I am trying to find the domain of this function f(x)=sqrt(x^2 - 2x +5). i am supposing that y=x^2 - 2x +5 and y must be greater of equal to 0. in otherwords where the graph is touching or above x axis. to find where the graph is touching x-axis i am trying to find the x intercept and i get...

When we solve to equations say y2 = 4x and x2 + y2 = 9/4 for x, we get two values - x=0.5 and x=-4.5 The equations represent a parabola and a circle resp. with x=either 0.5 or -4.5 as the abcissae of intersection. I don't understand why do we reject one value which is -4.5 in this case...

Homework Statement I don't know how to find the square root of a complex number in rectangular form? As in, say, \sqrt{}9-6i..my calculator can't do such an operation (yet my graphics calculator can, which can't be used in exams), so how do i go about to do this 'by hand'? I just found...

We can easily comment the result of a root operation just by the information if the degree of the root is odd or even. But what if the degree of the root (or power) is irrational? For example; -64 ^ \frac{1}{2} \, = \, j8 \,\,\,\,\, (imaginary) -64 ^ \frac{1}{3} \, = \, -4 \,\,\,\,\...

I need an algorithm to calculate nth root or power of any given real number. "n" can be either integer or fractional, and is real. I found http://en.wikipedia.org/wiki/N-th_root_algorithm" , but it requires to calculate power in it, therefore I can't use it. Newton's method: x_{k+1} =...

At http://www.wolframalpha.com/ , if you type: 1) (-1)^(1/3) It gives a complex approximation. Isn't it exactly -1? David

Homework Statement Show that the equation x3-15x+C=0 has at most one real root in [-2,2] Homework Equations Rolle's Theorem, and Intermediate Value Theorem. The Attempt at a Solution I showed that there is a root in [-2,2] by use of Intermediate Value Theorem. f(-2)<0 f(2)>0...

graph/analyze a function of a rational /w complex root?!? Homework Statement The function is y=x^2/(x^2+3) Homework Equations First and Second Derivatives Chart to find intervals of increase/decrease and concavity. The Attempt at a Solution 1) Domain {XeR} 2) Intercepts If...

a is a root of order k of the polynomial p provided that k is a natural number such that p(x)=[(x-a)^k]r(x), r is a polynomial and r(a) not equal to 0. Prove a is a root of order k of the polynomial p iff p(a)=P'(a)=...=[p^(k-1)](a)=0 and [p^(k)](a) not equal to 0. Note: [p^(k-1)](a) :=...

Hi, ive created several graphs in different emacs files. I now want to superimpose them using code in a different emacs file. This is what i have done: //get the input files TFile * inputfile = new TFile("p60.root","READ"); TFile * inputfile2 = new TFile("p20.root","READ")...

Homework Statement Calculate the area under the curve for the following: f(x) = √x*√(−32 − x) and g(x) = √(−x2 − 32x) Homework Equations The Attempt at a Solution I've been trying to do partial integration since the functions f(x)=g(x)area are mirrored, so they are equal...

Homework Statement * Show that the equation 2x-1-sinx=0 has Exactly one real root. Homework Equations *N/A The Attempt at a Solution *Ok so normally to find the real roots for x I would solve for x when I set the function equals to 0, but with this function there is an x...

http://www.macasex.com/ I saw a bit about this on TV [an investigative report, not a commercial] the other night. Apparently it is common for women in Peru to use Maca root to increase libido. When asked if it works, one women commented, "It will make Chinese fireworks in your pants!". It...

Homework Statement Im having difficulty drawing a specific graph. I am not entirely sure how to explain my question/ the graph i need to draw so i think the best way is to provide a bit of my code and explain using it the graph using it... the code below gives a read out of the energy...

ive been plotting 2D histograms (x vs y). when plotting using Draw->("surf"). it gives a 3D plot, showing the varying number of "hits" in each bin. I want to draw a TGraph which represents this so when drawing x vs y using Tgraph it gives a continuous line instead of a bunch of dots. I've got...

Hi everyone, I would please like some suggestions regarding where my error is, designing a lead compensator with the root locus method for a unity feedback control system where G = [12.5] / [2.5 1 2500]. I want to set the overshoot zeta = 0.5 for an overshoot of 16%, and settling time Ts =...

Homework Statement Really new to complex numbers so please forgive my ignorance. Prove that if the complex number z is an nth root of the real number x then the complex conjugate z (z with horizontal line on top) is also an nth root of x.Homework Equations i2=-1The Attempt at a Solution nsqr(z)...

Hi there, I have over the last couple of month worked my way through Algebra Demystified and College Algebra Demystified (well almost), and I just completed the chapter on polynomial functions and I’m stuck at one of the questions in the chapter review where I’m given a complex root and the...

Homework Statement integrate (xdx)/sqrt(1-x^2) on the integreal [2,5] Homework Equations integral u^n(du) = u^n+1/(n+1) The Attempt at a Solution I'm no good at using latex so I scanned in my work. I get .716 but when I check with my calculator it comes out as 2.863

z_k=\sqrt[n]{u}=\sqrt[n]{r}e^{i\left(\frac{\phi+2k\pi}{n}\right)}, k=0,1,2,...,n-1 and z_k=\sqrt[n]{u}=\sqrt[n]{re}^\frac{\phi+2k\pi}{n}, k=0,1,2,...,n-1 Which one is incorrect (note that in the first, e is out of the root)?

Homework Statement Antiderivative of sqrt[e^x+ln(x^2)+1] Homework Equations The Attempt at a Solution (2[(e^x+ln(x^2)+1)^(3/2)]x^2)/[3(e^x+2x)]

I tried to use tex code but it seems to be caching the image on preview, so anyway dy/dx ( x / root x) = 1 / ( 1/2 x^(-1/2) ) however the answer given to me is just ( 1/2 x^(-1/2). What's gone wrong? Spent an hour on this and now unsure if my algebra is wrong. And the tex code that I...

Square root of 4.1-- do you have to use calculus? In order to solve square root of 4.1, is there a simple arithmetic method or do you have to use calculus and use that "tangent line approximation formula"? I wonder how do calculators do it... does anybody know?

does anyone know any specific method to find the square root of a polynomial like : 4x4 + 8x3 + 8x2 + 4x+ 1 ?? thanks in advance!

Homework Statement y'' -2y' +5y =0 , y(0)=1, y'(0)=1 you get a complex root conjugate. Homework Equations y=e^(rt) y'=re^(rt) y''=r^2 * e^(rt) The Attempt at a Solution I have in my notes sin(omega*t)e^(sigma *t), cos(omega *t)e^(sigma). I don't think i took down the notes...

Homework Statement If p is prime \sqrt{p} is prime. Are there flaws in my proof ? Homework Equations The Attempt at a Solution Assume \sqrt{p}=\frac{m}{n} and gcd(m,n)=1 p = \frac{m^{2}}{n^{2}} Since p is an integer n^{2}|m^{2} but gcd(m,n)=1 Therefore...

Homework Statement if n>1, prove that \sqrt[n]{n} irrational Homework Equations n/a The Attempt at a Solution so suppose it is rational, so i know \sqrt[n]{n} must be integer, say p then n=p^n and how do i prove this is not true?? i can prove if p>1 then p^n>n for all n>1 by induction...

Homework Statement Prove the following limit: lim_{n \rightarrow \infty } n^{ 1 / n } = 1 Homework Equations Not sure. The Attempt at a Solution Given any \epsilon > 0, choose N \in \mdseries N s.t. \left| n^{ 1 / n } - 1 \right| < \epsilon for all n > N I am not sure...

Homework Statement [PLAIN]http://www4a.wolframalpha.com/Calculate/MSP/MSP184619c56eg84971107d00001e292h4340heh8g4?MSPStoreType=image/gif&s=35&w=135&h=53 It is a definite integral between x=0 and x=20. I forget how to integrate with a square root. Do you just change it to a power of a...

Homework Statement Integrate : f(t) = t3/ sqrt(t2+1) Homework Equations The Attempt at a Solution t2* t / sqrt(t2+1)let u = sqrt(t2+1) u=(t2+1)0.5 u2 = t2 +1 t2 = u2 -1 -Eq 1u=(t2-1)0.5 du = t/sqrt(t2-1) dt dt = sqrt(t2-1)/t du -Eq 2 Hence Substituting 1 and 2...

Homework Statement Find the length of x=y^3/30+5/(2y) on 3 <= y <= 5 Homework Equations L = integral sqrt(1+(dx/dy)^2)dx The Attempt at a Solution I got to the integral upper bound = 5, lower bound = 3, sqrt(y^4/100+25/(4y^4)+1/2)dy. How do I actually solve the integral? It...

And if so, could I take the ith root of i?

How to solve recurrence relation with one real root and two complex roots ? The Example is ; Solve the recurrence relation a n-1 + a n-3 = 0 where n ≥ 3 and a 1 = 1 a 2 = 1 a 3 = 2 a n = nth order a n-1 = (n-1)th order. a n-3 = (n-3)th order. I've started the solving ; a n = r^n so...

sorry, I am using phone, owho i hope you can get it. suppose its rational. in the form a/b gcd(a,b)=1 and so and so and so and then they concluded that a^2=2 is a contradiction. but i cannot see what it conradict the assumption. help

hi, I am plotting a 1D graph in root (TH1F pointer). currently the y-axis gives the number of entries in each bin along my x-axis. how do i change it so that it is actually the number of entries in each bin divided by the total number of entries. thanks

Hi all, I am trying to find a nice back-of-the-envelope way to numerically-calculate nasty things like square roots and stuff. For instance: \sqrt {4.51} = ? I tried to use a linearization: \sqrt x = \sqrt {n + \varepsilon } = \sqrt {\left[ {{\rm{integer}}} \right] + \left[ {{\rm{decimal...

Hi there, I am having difficulty with one aspect of intergration by substitution where the substituion of a square root is U^2, wondering if anyone can help. Problem: Integral of: 2x√(3x-4) dx by substituting U^2 = 3x-4 Would du^2/dx = 3 therefore 1/3 du^2 = dx (I think...

Given a symmetric 2x2 matrix, what would be the way to calculate the square root of it? Here, http://www.jstor.org/stable/2689616?seq=2 , it is announced that a relatively simple formula could be applied for the resulting matrix entries, but I could not access it further. Thanks

Homework Statement Evaluate the next integrals, expressing it previously in the forms that contains \sqrt[ ]{a^2+u^2}, \sqrt[ ]{a^2-u^2} and \sqrt[ ]{u^2-a^2}, and then solve it using the integral table; The exercise which I couldn't solve...

Is square root a function in this way? f:\mathbb C\rightarrow\mathbb R^+ However contradiction can be drawn:\sqrt{x^2}=|x|\text{ and } i^2=-1 \sqrt{-1}=\sqrt{i^2}=|i|=1 \sqrt{-1}=1 ??What is the problem in the...

Homework Statement dP/dt=root of (Pt) Homework Equations P(1)=2 The Attempt at a Solution Well, I figure that the integrating factor is 1, since there is no P(x) value, so it's a matter of finding the integral of root(Pt). I can't solve this because the only method I know is...

1. square root of 144400 using Taylor series 2. I used the equation of sqrt(x) for x>2 given in http://www.understandingcalculus.com/chapters/23/23-1.php 3. I have tried it upto the 7th power and I got sqrt(144400)=1/0.209482810=4.773661 I know sqrt(144400)=380; and...

Homework Statement If Kp = 6.0 x 108 For equilibrium N2 <--> 2N Then what is the equilibrium constant of N <--> .5N2Homework Equations K= C^c/A^aThe Attempt at a Solution I tried finding the fourth root of 6.0 x 108 and that didn't give the right result. BTW the answer is 4.1 x 103, I'm...

Homework Statement Hi guys, I'm doing a rather long math modelling task. As part of the task, I have to investigate the following argument: There is a rectangle ABCD. It is sliced by the line EF, such that EF is parallel to AD and BC. M is the midpoint of BC. X is a point on the line...

Hi, I ve got two problems. 1) The problem i have is how to find an open loop transfer function that gives poles at -3, -6, -7+_ j5 and zero at -5. So i think that the numerator is (s+5), and denominator has (s+3),(s+6). and now I don't know how to carry on. Is it ( s+7+j5) and (s+7-j5)?. Am I...

Homework Statement Let q=p^e, where p is a prime and e is a positive integer. Let a be in GF(q). Show that f(x)=x^p-x+a is irreducible over GF(q) if and only if f(x) has no root in GF(q) Homework Equations The Attempt at a Solution One of the directions seems obvious. Namely, if...

Homework Statement Let F have prime characteristic p and let a be in F. Show that the polynomial f(x)=x^p-a either splits or is irreducible in F[x]. I was given a hit: "what can you say about all of the roots of f in a splitting field?"Homework Equations The Attempt at a Solution Suppose f...

Is it a right mathematical operation (a*b)^0.5 = a^0.5 *b^0.5 when a and b either both are negative or one of them is negative.

Homework Statement So I was doing the following relativity problem: An atomic clock moves at 1 000 km/hr for 1 hr as measured by an identical clock on the Earth. At the end of the 1 hr interval, how many nanoseconds slow will the moving clock be compare with the Earth clock? The problem...