Roots Definition and 962 Threads

Question that I came across and that has stumped me for about a week hehe. Let p(z)=z^n +i z^{n-1} - 10 if \omega_j are the roots for j=1,2,...,ncompute: \sum_{j=1}^n \omega_j} and \prod_{j=1}^n \omega_j}

for sqr root of (n + sqr root (n) ) - sqr root (n),is the answer = zero or infinity so converges or diverges??

find all solutions of the given equation: (z+1)^4=1-i im not sure if i did this right, but here's what i did the first thing that i did was notice that 1-i = 2^1/2 * (cos (pi/4) + i*sin(pi/4)) then i found z= [2^(1/2*1/4) * (cos (pi/4) + i*sin (pi/4) )^1/4] -1 then using de moivre's thrm...

Does anyone have insights or a perspective on the possible biological roots of PA behavior (or disorder)? I am not a psychologist, psychiatrist, or biologist, but when I think of the evolution of the species it kind of seems obvious that the mammals lived a hard life under the dinosaurs' feet...

Since one can construct the length of a non-integer square root by drawing accurate triangles, and can draw a circle with a circumference of pi, then shouldn't one be able to plot corresponding non-integer square roots and pi on a number line? I know these numbers are supposedly irrational, but...

I have the definition that if F is a finite field then a \in F is a primitive root if ord(a) = |F|-1. Now what I don't understand is how exactly are there \phi(|F|-1) primitive roots? (Note: This material is supposed not to use any group theory.)

If ar^2+br+c=0 has equal roots r1, show that L[e^(rt)]=a(e^(rt))``+b(e^(rt))`+ ce^(rt)=a{(r-r1)^2}e^(rt) could someone offer some advice?

All the roots of a real function f(x) are real unless. 1.K(x) is a Polynomial of degree k 2.f(x)=exp(g(x)) where g(x) is different from ln of something 3.f(z) with z=u+iv is invariant under the transformation of v=-v with f(u+iv)=F(u-iv).. 4.the function f includes some of the functions...

I'm not sure whether this is the correct forum, so I apologise if it's in the incorrect forum. Anyway, when studying A level maths a few years ago, we came across a technique for calculating roots that my teacher claimed was used before calculators were invented. I can't remember the actual...

why is it that when you have the same roots to an O.D.E., you usually add an x or x^2 to get a basis?

Hey having a bit of trouble with this question, not sure what to do! QUESTION - express the fraction in the form a + b rootc / d 3 + root24 / 2 + root6 ------------------------------------------ (3 + root24 / 2 + root 6) x (2 - root 6 / 2 - root 6) Simplifying gives (6 -...

Ok, i got two funktions: b1:=(x/10)+sin((x/3)+(Pi/2)); and b2:=(1-2*cos((x/4)+(Pi/2))); I need to determine all the roots between 0 < x > 30 If I plot the functions i see that there should be two roots plot([b1,b2],x=0..30); But when try to get maple to calculate the roots It only...

hello how can i finding roots to cubics?? explain by example :smile:

let be the function f(x) so we have that if x is a root also x* is a root, but we have that x is NEVER a pure imaginari number,i mean x is always different from x=ia the my question is if this means that all the roots will be real,the only counterexample i find is...

x^2 +6x +k=0 has one root (a) where I am (a) =2, If k is real find both roots of the equation and k So i got b+ 2i is the root (b+2i)^2 +6(x+2i) +k=0 and after expanding it out, i have no clue what to do. Please help. THanks

How would I go about finding a number that is a primitive root modulo 125? There definitely exists a primitive root since 5^3 =125 The problem basically comes down to finding 'a' (primitive root); a^50 congruent to -1 (mod 125) Anyone know a way apart from trial and error? Thanks

I am in a Systems and Vibrations class but am currently doing differential equations. A problem I am doing requires me to find the transfer function [X(s)/F(s)] and compute the characteristic roots. So far I have: X(s)/F(s) = (6s +4)/(s^2+14s+58) That is the transfer function but now...

If m, n, and 1 are non-zero roots of the equation x^3 - mx^2 + nx - 1 = 0, then find the sum of the roots This is what I did.. m, n, 1 are the roots. m and n not equal to 0 x^3 - mx^2 + nx - 1 = 0 f(m) = 0 --> m^3 - m^3 + mn - 1 1 = mn (1) f(1) = 1 - m + n - 1 = 0 ... m = n (2)...

In seeing various related topics in PF regarding the reasons for terrorism, solutions for terrorism, the effects of the Bush administration on our country and the world, and more recently nuclear proliferation via the Bush Doctrine, I thought I’d start this new thread, which also may provide...

Can a number have more than 1 primitive root? Thanks

Hi, I came across this puzzle, see if you can solve it :smile: : \sqrt{1 + \sqrt{1 + 2\sqrt{1 + 3\sqrt{...}}}} = ?

let be the quotient: Lim_{x->c}\frac{\zeta(1-x)}{\zeta(x)} where x=c is a root of riemann function... then my question is if that limit is equal to exp(ik) with k any real constant...thanks... the limit is wehn x tends to c bieng c a root of riemann constant

Hi all Jut had a question. How do I go about finding the general formula for roots of the complex poly {z}^{n}-a where a is another complex number. Do I just go {z}^{n}=a? :S so complicated this things! Thanks in advance!

Let be the function h(x)=f(x)+g(x) we want to obtain the values of x so h(x)=0 and we have that f(x) and g(x) have the same roots (if a is so f(a)=0 then g(a)=0 too) so we have two types of roots: 1.-values of x that satisfy f(x)=-g(x) 2.values x that make f(x)=g(x)=0 then we make in the...

There are n nth roots to every complex number (except zero). My question: How many "roots" are there when you take a complex number to an irrational or transcendental number. For that matter, how do we define raising a number to an irrational number? How do we define raising a number to a...

Q. Fix n>= 1. If the nth roots of 1 are w_0,...,w_(n-1), show that they satisfy: \left( {z - \omega _0 } \right)\left( {z - \omega _1 } \right)...\left( {z - \omega _{n - 1} } \right) = z^n - 1 I tried considering z^n = 1. z^n = e^{i2\pi + 2k\pi i} \Rightarrow z =...

This may be a bit silly but i forget how to factor this into complex factors: s^2 + 6s + 25 i know the answer is (s +3 - i4)(s +3 - j4) but how do i get that?

I was curious about what class would cover those types of Linear DE w Constant Coeff, particularly Hyperbolic Functions and exp z type of things. I remember my lecturer said back in Intro DE that we only covered first 2 types of Auxiliary Equations - real distinct roots and real repeated ones...

Problem: If c_{1}, ..., c_{n} are the complex roots of a_{n}z^n + a_{n-1}z^{n-1} + ... + a_{1}z + a_{0} = 0 with a_{n} not 0 and S_{k} is the sum of the products of these roots taken k by k, then S_{k} = (-1)^k . \frac{a_{n-k}}{a_{n}}. Prove this by using induction. So for n = 3 this...

Hi, How is the roots of a quadratic equation related to the distance from the x-axis at where the root is - where ... ax^2+bx+c=0 and ... x = (-b +- SQRT(b^2-4ac))/2 Can someone help me to establish where this distance relationship to the x-axis and the root come from? Thx! LMA

Hi, A cubic equation has at least one real root. If it has more than one why are there always an odd number of real roots? Why not an even number of real roots? Can someone help me to prove this? Thx! LMA

I've been trying to derive general solutions for cubic roots, i.e. the general solutions of (will Latex just work?) $ax^3+bx^2+cx+d=0$ I do not want to be shown the solutions - but does anyone know what direction to go into achieve this? I thought I'd found solutions at one point but...

Hi guys, can anyone tell me how I would go about solving this equation? : x^5 = x Rearranging it gives: x^5 - x = 0 But then I don't really know what to do next. I know just from looking at it and thinking about it that the roots should be x = 0, 1, -1, -i, i...but I need to be able to...

What are some good quick ways to Extract Square Roots in your head. I'm looking for a method that is very prescice and easy thanks, hopefully somebody helps me out

hello. I was wanting to know how to raise a number to any power without using a calculator. More specifically, I was wanting to raise numbers to the .5 power, (and all the other roots, 1/2, 1/3, 1/4). How can this be done? <----------------------> My fellow 633|<5 :smile:

this problem is annoying. I've found that the primitive roots of 9 are 2 and 5. since 2|18 it can't be a root. i know via some theorems in my book that if 5 is a primitive root of 3, then its a primitive root of 3^k, and also of 2*3^k. sorry about not using latex, shouldn't need it for...

solve \sqrt2 \sin\theta= \sqrt3-\cos\theta algebraically for the domain 0<theta<2pi I know that the cos can be changed into 1-sin^2 theta but I don't know what to do after how do I get everything on the right hand side and simplify it?

In math class today, we were discussing quadratic residues, and one of the things that came up was the fact that x^n-a=0 has n roots. This just made me start thinking about real and complex roots. A question that I had was whether, given n>2, is it possible to have n real roots in...

I'm working with a professor on a project and we are going through a bunch of integrals in the "table of integrals series and products" and there is one that we cannot seem to get--the answer in the book is wrong after doing some numerical calculations, but we can't find a "solution" to the...

I have three problems that I can't seem to solve. I was wondering if anybody could help me or explain to me how to solve these. Note: * = multiplication. 1. (6^1/2 * 2^1/3)^6 2. ^4√7 + 2^4√1792 3. 3(X-4)^1/2 + 5 = 11

How can I estimate the value of sqrt. of a particular no. which is not a perfect square(e.g. 125) without using the calculator? Secondly how does the Calculator solve it? Does it use logrithms? If it does how does it solve them?

We have to find the max/min of a derivative and we can't figure out how to find the roots of the function. The equation is y'=-5x^4-7x^2+10x+4. We tried factoring, but that won't work, the quadratic equation doesn't work, and we don't know how to solve for x. :cry:

roots! HELP For what values of k does the equation x^2+k=kx-8 have two distinct roots, one real root, no real roots? convert into standard form first well x^2+k-kx+8 I don't know if i can simplify this further? and if i can't then what does a=? b=? and c=? I don't understand how to do...

Hey guys can you help me solve this problem: Find all real numbers a with the property that the polynomial equation x^{10} + ax + 1 = 0 has a real solution r such that 1 / r is also a solution. Thank you for helping me :smile: Sry I have posted this problem once before, but nobody helped...

How do we do this? I know how to find all RATIONNAL roots but what about the irrationnal ones? [tex]2x^5-5x^4-11x^3+23x^2+9x-18=0[/itex]

Ok so I know that when you have radicals such as the following you only have one answer right?... x + 1 - 2(square root of [x+4]) = 0 ok so x = 5 right?... i don't know why but it just does... I can't solve it If i solve it It works looks like this: (squaring everything I...

I need to factorise x^3 + 216 to include (x+6): (x + 6) \ (x^3 + 216) (lim where x approaches -6) I broke it down to (x + 6i)(x^2 - 36i) ... but that's no good.

I've got a homework problem from my function theory course that I never fully understood. It's getting hot again since the exams are nearing...please help :smile: It goes simply like this: Compute the Integral \int_{\vert z \vert=1}\frac{dz} {\sqrt{6 z^2-5 z +1}} The square root is chosen...

Please look at the attached pdf http://www.geocities.com/complementarytheory/Roots-Chain.pdf . By this model we can see that √1 is the "shadow" of √2 and √2 is the "shadow" of √3. If we can conclude that √3 is the "shadow" of √4 ... and so on, then do you think that this "Chain of...

Why do we have anti-West terrorism stemming from the Middle East? Why do they have hatred for Westerners? I have heard the idea that it's becase they hate us for being great and successful and sugar and spice and are jealous to the point of nausea. I think that this is nothing but a...