Roots Definition and 962 Threads

w_{n} is primitive root of unity of order n, w_{m} is primitive root of unity of order m, all primitve roots of unity of order n are roots of Cyclotomic polynomials phi_{n}(x) which is a minimal polynomial of all primitive roots of unity of order n , similarly, phi_{m}(y) is a minimal...

Need Assistance w/ existence of conjugate roots in polynomial Prove: given that f(x) = Anx^n + An-1X^n-1+ ...A1X + A0 , and An does not = 0 => if f(x) has a root of the form (A+Bi), then it must have a root of the form (A-iB). (complex roots) So far I've come up with the conjugate roots...

All right, thanks to everybody's help, I've got the algorithm for determining the nth roots of unity. However, for determining which ones are primitive, I'm still having a little trouble. If n is odd, I can test if (n, k) are coprime. However, for even values of n, it seems that it doesn't...

Hi eveveryone I was just hoping for some quick help on frustrating physics related math problem. I won't go into detail on the actual problem becasue i know i found the correct polynomial but i was wondering if there was any easy way to find the roots to this polynomial...

(*)p(x) = x^4 + ax^3 + bx^ 2 + ax + 1 = 0 where a,b \in \mathbb{C} I would like to prove that a complex number x makes (*) true iff s = x + x^{-1} is a root of the Q(s) = s^2 + as + (b-2) I see that that Q(x + x^{-1}) = \frac{p(x)}{x^2} Then to prove the above do I then show...

Where can all the classic papers by the experimentalists that layed the foundation for nuclear physics be found?:confused: Rutherford, joliot-curie, fermi, lawrence, Hahn ect. Im very interested in reading exactly how they setup there experiments, the conclusions they drew and so on.

For the function ## y=f(x) ## is there a test to prove if its roots are real or either has some complex roots?, or in more general cases: ## y=g(x)D^{k}f(x) ## k>0 and a real D=d/dx number.:rolleyes: :rolleyes: The question is that sometimes it can be very deceiving to tell if a function...

of the equation z= exp(-z) could someone possibly point me in the right direction to start this problem? this area of math is still new to me so please go easy thanks

I just have two questions: A fundamental problem in crystallography is the determination of the packing fraction of a crystal lattice, which is the fraction of space occupied by the atoms in the lattice, assuming that the atoms are hard spheres. When the lattice contains exactly two...

hi, is there any way to find the cube roots of a complex number WITHOUT converting it into the polar form? i am asking this because we can find the square root of a complex number without converting it. i was just wondering whether there is such a method for finding cube roots too. i was...

Prove that the sum of the roots and product of the roots of the equation ax^2 + bx + c = 0 are -b/a and c/a respectively thank you

Question: How many real roots does the equation x^5 + x + c = 0 have on the interval of [-1,1]? I try to differentiate the equation, then I obtain 5x^4 + 1. When at its local minimum or local maximum, 5x^4 + 1 = 0. So, there is no solution for the equation, since 5x^4 + 1 > or = 1...

The Roots and degree of a polynomial function are given. Write the function in standard form. b) 2, -2i, degree 4 obviously i know there is a function with x^4 and it should have 4 x answers so I don't know how to do this...I know that (x-2) is a factor

the book asks to fnd the four roots of z to the fourth power + 4 = 0 and then use to demonstrate that z to the fourth power + 4 can be factored into two quadratics with real coefficinets. I am clueless on where to start. Please help.

I just bombed a quiz because it was 2 questions and this was one of them: Find all three complex roots of the following equation (give answers in polar and rectangular form) z^3+8=0 Looks easy enough, z=2e^{-i\frac{\theta}{3}} This is where I think I completely realized I wasn't sure what...

I have a feeling the answer to my question is pretty simple, but I couldn't come up with an answer, so I'm going to ask it here. Say you have an equation which looks like this: y^2 = x + 4 Assuming you want to rearrange the equation to solve for y, you would do this: y = square...

How to solve cube roots question ? Example : x^3 - 100x^2 - 7800x + 16300 = 0 I had think long time but still cannot find the way. Besides trial an error, is there anyway to solve this problem ? thank you.

I am stuck half way in solving this problem (the square root nominator confuses me) :confused: : http://img235.imageshack.us/img235/8459/1mi1.jpg and I cannot get it to match the answer given on the back of the textbook: http://img235.imageshack.us/img235/7041/answerop5.jpg Please...

Now this bugs me. First there were no negative numbers. Then there were no square roots to negative numbers. Then every real number had two square roots, but no word on imaginary numbers. Luckily for me, I had a calculator that told me the square root of i wasn't some other type of number or I...

Is there a way to find the,"Sum of the square roots of the first n natural numbers"?

i wonder if there's a formula like for quadartic and cubic equations also for roots polynomials, like this equation: ax^(1/2)+bx+c=0 or like ax^(1/3)+bx^(1/2)+cx+d=0 ? and what are they?

there is a way of calculating the square root of any number (without using a calculator of course). is there a similar way, or any way, in fact to calculate cube roots, fourth roots, etc. again without using a calculator??

for x^2 +4x +5=0 ,may i know how to compute the roots incomplex form?? the answer is -2+j and -2-j thanx

http://album6.snapandshare.com/3936/45466/776941.jpg PS. Just wanted to say thanks for all the help so far. This is a really great forum and I am receiving tons of help. I like how people here are not just blurting the answers, but are actually feeding me ideas so that I may work them out...

Let,s suppose we wish to calculate the roots of a function f(x) f(x)=0 , of course you will say.."that,s very easy doc...just try Newton Method, fixed-point method or other iterative method"..the main "problem" we have is if f(x) includes non-differentiable functions such us the floor function...

Is there a good algorithm for computing such things modulo a prime? (I'll confess to not yet having tried to see if Shanks' algorithm can be easily adapted; I'll probably fiddle with that tomorrow)

If we define the function: F[w]=\int_{-\infty}^{\infty}dxe^{-iwx}g(x) my question is..what would be the criterion to decide if F[w] has all the roots real (w=w*) and how is derived?..thanks.

Considering the case of cubic polynomials with integer coefficients and three real but irrational roots. Is it true that it's impossible that all three roots can be in the form of simple surd expressions like r+s \sqrt{n} (where r and s are rational and sqrt(n) is a surd). The argument is that...

It,s proven that there can not be any Polynomial that gives all the primes..but could exist a function to its roots are precisely the primes 8or related to them) if we write: f(x)=\prod_{p}(1-xp^{-s})=\sum_{n=0}^{\infty}\frac{\mu(n)}{n^{s}}x^{n} wher for x=1 you get the classical...

Hello, I have two questions about this problem: (D^4 + 5D^2 + 4)y = 0 y(0) = 10 y'(0) = 10 y''(0) = 6 y'''(0) = 8 \lambda^4 - 5\lambda^2 + 4 = 0 (\lambda^2 + 4) (\lambda^2 + 1) Until here I am fairly sure that I didn't mess it up.. But I'm not sure if I have the roots...

this is a question that only mathematicians know about why the roots of the Polynomial: \sum_{n=0}^{k}a_{n}x^{n} with k>4 and integer can,t be obtained by elementary algebra (addition,substraction,and so on)..

Okay, before I start my discussion, note that k \in \mathbb{R} Edit: for anyone reading this right now, I accidentally hit 'submit post' instead of 'preview', so please ignore the thread until it has some content! Okay, here is the content. In my prof's notes, he is evaluating...

Please Help! I designed this "PROGRAM"! TO calculate the real roots of a quadratic equation... but the compiler miracle C kept saying there's something wrong around the "if" word... saying "unrecognised types in comparison" it seem SO FINE to me... what is wrong?!:eek: #include...

This is indirectly related to issues with cyclotomic polynomials and glaois groups. Is there some easy way to know if you are dealing with a cos or sin that is expressable in terms of roots of rationals? Like \pi/3 for example? If so, is there any straightforward way of figuring it out...

The first one, integration, I just want to check my answer. \int \frac{1}{64} (\cos6\theta + 6\cos4\theta + 15\cos2\theta + 20) = \frac{1}{64} (\frac{\sin6\theta}{6} + \frac{6\sin4\theta}{4} + \frac{15\sin2\theta}{2} + 20\theta + c I just wasn't sure if the integral of a constant wrt theta...

http://img522.imageshack.us/img522/7522/mat4vj.gif where X is the number into the term http://img524.imageshack.us/img524/2985/prob23ei.gif Computer F'(6) The square root is what's giving me my most difficulty. I don't know how to apply the term with a square root and computer f'(6)...

can roots be at the same points as POI's? because when I set my original equation to zero and I set my second derivative equation to zero i get the same answer? is it possible that roots can be same as the POI's.

Hello, I have a few questions! I need clarification on certain points that were not very clear in my calculus book. ---------- Question 1: I know that \int e^{ax} dx = \frac{1}{a} e^{ax} But how do you integrate \int e^{ax^2} dx ? ----------- Question 2: I know that...

Prove x^4 + 4x + c = 0 has at most two real roots My thinking is that to prove this I would assume that it has three real roots and look for a contradiction. So I set f(x) = x^4 + 4x + c and assume three real roots x_1, x_2, x_3 such that f(x_1) = f(x_2) = f(x_3) = 0 By MVT I...

I have two problems I'm working on that I can't figure out. Could anyone please help? 1. show that if p and q are distinct odd primes, then pq is a pseudoprime to the base 2 iff order of 2 modulo p divides (q-1) and order of 2 modulo q divides (p-1) I've been trying this proof by...

I was curious why primitive roots are so important? Also, how one would find out if a number has a primitive root and what and how many of them they are?

is there a method to compute roots other than sqrt?, like 10th root or 13th root of a number? and, what are they?

find the four roots of the equation z^4 + 7 -24i = 0 completely lost, some help please...

It is me again, 2 problems later I ran into another problem, I've submitted it a few different times but still is incorrect. Anyone see my mistake? I entered this as the answer: http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/a0/13092fac04d4a01ec22b57e193ed051.png Here is the...

i am to find the 4th roots of -16 (-16)^{1/4}=2i^{1/4} i=e^{i \pi/2} i^{1/4}=e^{i \pi/8} (-16)^{1/4}=2e^{i \pi/8} or (-16)^{1/4}=2e^{i 5\pi/8} or (-16)^{1/4}=2e^{i 9\pi/8} is this correct?

OKay i havn't gotten 1 2nd order Diff EQ right yet! I'm on a role! wee! Find y as a function of t if 81y'' + 126y' + 79y = 0, y(0) = 2, y'(0) = 9 . Here is my work: http://img204.imageshack.us/img204/4605/lastscan5ag.jpg I submitted this and it was wrong...

Hello everyone. I"m not getting this problem right. <insert sad face here> Find y as a function of t if 6y'' + 33y = 0, y(0) = 8, y'(0) = 5 . y(t) = hokay, here is my work, it is sloppy sorry. Can you see any obvious mistakes I made? Note: the sqraure root should be encompassing both the 11...

I am asked to use the exponential form e^{i \theta} to express the three cube roots of: (a) 1 (b) i (c) -i what exactly does this question mean? I am really lost as to what they are asking for. here is a stab at it: (a) cube root of 1 is 1... so... would that mean... 1=e^{- \infty...

i'm doing my online homework as we speak and they problem I'm on is this Use your calculator to find the square root of 6.70 × 10^-19 and i calculated that problem in my calculated and i got 6.7e^-19 and i typed it in my homework and its giving me an error and saying "This question...

Hello All I am trying to figure out how to determine if there are two, one, zero, or infinitely many roots for given formula ax^2 + bx + c. Are there any easy ways to determine this without having to use the quadratic formula? Thanks P