Roots Definition and 962 Threads

How many complex roots admit the following equation: (2 z^2 + 1)^2 ((z + d)/(z - i))^1/2 - (2 z^2 - d)^2 ((z + i)/(z - d))^1/2 == 0 for 0 < d < 1, where i = (-1)^1/2. Can I found how their number varies with d by using the argument principle? Thanks in advance for helpfull suggestions

Homework Statement (all this is included in the attachment, btw) p(z)=z^4+4.25*z^2+1 1. use MATLAB to find the four roots Ck of p(z)= 0 2. For all complex constants ck (different than Ck) define the complex valued function Z(t)= 4\Sigmak=1 ck*exp(Ck*t)...

is the light doppler effect a purely relativistic effect? or it is present even in the classical limit?

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...

Hi, If anyone has a copy of this book, I'm just struggling to understand a point in the chapter about Lie Groups. In particular the section on qunatization of the roots, on p177-178, he generates the diagrams in fig 9.2 from those of 9.1. I thought I understand this, but I don't understand...

Homework Statement In each of the following items approximate the zeros of f using Newton's method. Continue iterating until making two successive approximations differ at most in 0.001. The Newton iteration: x_{n+1}=x_n-\displaystyle\frac{f(x_n)}{f'(x_n)} Well, I have a doubt about this. I'm...

Homework Statement Solve y''+4y'+5y=0 find solutions for y(0)=1 and y'(0)=0 Homework Equations Quadratic equation The Attempt at a Solution Hows this look ? assume solution is in the form of y=ce^{rx} substitute y=ce^{rx} into the equation...

Plant roots absorb water and nutrients for the life of the plant. What keeps the exterior surface of the root cells from becoming clogged...say with dirt or other matter. Any filter eventually becomes clogged and needs to be cleaned, how about plant roots? One possibility is that surface...

Homework Statement I am trying to get the roots of: (x-a)^3 - (x-a)b^2 - 2b^3 -2b^2(x-a) which I know they are x = a-b and x = a+2 b the problem is, how can I reach that solution ? The Attempt at a Solution At first I thought of separating the independent term (the one...

Homework Statement Use the disciminant to determine all values of k that would result in the equation x^2 - kx + 4 = 0 having equal roots. Homework Equations x = -b +/- (square root) b^2 - 4ac and divide by 2a or b^2 - 4ac The Attempt at a Solution a = 1 b = - 1 c = 4 I'm...

Homework Statement I need to prove that the following limit holds when \sqrt{s}>>m \log\left(\frac{\sqrt{s}+\sqrt{s-4m^2}}{\sqrt{s}-\sqrt{s-4m^2}}\right) \rightarrow \log\left(\frac{s}{m^2}\right) The Attempt at a Solution I've tried several manipulations using logarithms properties but had...

I've never properly studied complex numbers but I will soon (in September). Basically: We get taught from a young age that: the real root of f(x)=x²-4 is where the graph of y=f(x) cuts the x axis But is there a graphical representation of a complex root? What's so special about the...

Homework Statement Let x1, x2, x3 are the roots of the polynomial f(x)=x3+px+q, where f(x)\inQ[x], p\neq0. Find a polynomial g(y) of third degree with roots: y1=x1/(x2+x3-q) y2=x2/(x1+x3-q) y3=x3/(x1+x2-q) Homework Equations The Attempt at a Solution Any ideas? Thank you.

[2(cos(pi/3)+isin(pi/3))]1/2 I simplified it to 21/2(cos(pi/6)+isin(pi/6)), but I have no idea what else to go to. Any tips would be very helpful, thx in advance

I'm trying to prove that a polynomial function of degree n has at most n roots. I was thinking that I could accomplish this by induction on the degree of the polynomial but I wanted to make sure that this would work first. If someone could let me know if this approach will work, I would...

Let f (x) = (x^2 − 1)^n . Prove (by induction on r) that for r = 0, 1, 2, · · · , n, f^ (r) (x)(the r-th derivative of f(x)) is a polynomial whose value is 0 at no fewer than r distinct points of (−1, 1). I'm thinking about expanding f(x) as the sum of the (n+1) terms, then it's easier to...

Hey guys, I've been working on this computer application, and ended up needing to compute the roots of a quartic equation. So I implemented Ferrari's method and the results for the most part are working, however I've come across a few exceptions where I'm getting incorrect results. For...

Homework Statement How do i solve this integral ? \int \big( \sqrt{x^{3}+1} + \sqrt[3] {x^{2}+2x} \big) \ dx Homework Equations The Attempt at a Solution what is the appropriate substitution to make here

Is there a function in Matlab which gives a list of numerical approximations to the roots of a polynomial equation (eg. like NSolve in Mathematica?) Thanks!

I'm currently in Seoul, Korea. My last blog here warned I might be gone for a bit, but I have internet at my current accommodation, so here's a hi! You can find out more about why I might be in Korea from my very first blog entry: https://www.physicsforums.com/blog.php?b=1316 . I've come home...

Homework Statement Find the range of the number k so that the equation 100^x-10^(x+1)+k=0 has two distinct positive roots Homework Equations The Attempt at a Solution I know if it says for two distinct roots only , k<25 but now its two distinct POSITIVE roots , so how ?

Homework Statement i) Solve the equation z^3 = \mathbf{i}. (ii) Hence find the possible values for the argument of a complex number w which is such that w^3 = \mathbf{i}(w*)^3. I'm stuck on part ii. Homework Equations The Attempt at a Solution The answer to the equation in...

Homework Statement The quadratric equation x^2 - 5x + 7 = 0 has the roots α and β. Find the quadratic equation with roots α^3 and β^3. Homework Equations N/a The Attempt at a Solution u = α^3 α = u^(1/3) u^(2/3) - 5(1/3) + 7 = 0 u^(1/3)[u - 5] = -7 --- minus 7 off each...

Let's say we have: A=B3 r=6B2 and we want to rewrite A in terms of r. My way to do it is: B2=r/6 => B=+-\sqrt{(r/6)} => B3=+-(r/6)\sqrt{(r/6)} => A=+-(r/6)\sqrt{(r/6)} In a book I found...

Lt (1 – 1/√2)* (1 – 1/√3)…… (1 – 1/√n+1) n->∞ There must some simple calculation to find this, but I cannot get this, limit exists since each tern is less than 1, and limit is more than 0. so limit exists between (1 0).

Homework Statement What are the roots of z^n = -1 Homework Equations The Attempt at a Solution are they e^{\frac{2\pi k i}{n}-\frac{i \pi}{n}} ?

Why is it said that an equation of nth degree must possesses n roots ? if x^1 = y, x has only 1 value x^2 = y, x has 2 values (the 2 values may be equal) x^3 = y, x has 3 values going on like this, we have, x^0 = 1 , implies x has no solutions. but x has infinite number of solutions.

Homework Statement F(X)=√x F((F(2)-2)^2)+f(2) Homework Equations The Attempt at a Solution I get to √(-4√2 +8) ... that minus sign is annoying me =] any help?

I was wondering how the general formula for the solutions of an nth order linear homogeneous ODE that had a characteristic equation which could be factored to (x-a)^n was derived(IE a set of solutions consisting e^(mx), x*e^(mx), ...x^(n-1)e^(mx)))? For example the ODE, y^(3)- 3y'' + 3y'...

Homework Statement Find the solution of the initial value problem. x'=[3 9; -1 -3]x, x(0)=(2 4)T Homework Equations A good guess should be x=tert$ + ert# The Attempt at a Solution But ... the only root is r=0, which gives me a solution x(1)(t)= C1(-3 1)T. Using the...

I have a function : f (n)=40*n^1.5-875*n+35000; How can i solve this equation with MATLAB. I know how to solve polynomial equation but this is different i think.

ok, for 2nd order differential equations, if we have repeat roots, like for example y" +4y = cos2x , we would have repeat roots +2i,-2i. so how do we try for the particular solution? i tried Acos2x + Bsin2x, it all canceled out. i tried (Ax+B)cos2x + (Cx+D)sin2x it all canceled out too then...

Homework Statement Let w be a primitive cube root of 1. show that 1, w,w^2 are the three cube roots of 1. Homework Equations The Attempt at a Solution I'm not quite sure how to even start this. any help will be greatly appreciated.

Find six distanct sixth roots of -1 + i root 3 I want check my answer ==== > x = -1 y = root 3 r = 2 tan Q = 2pi/3 -1 + i roo3 = 2 { cos ( 2 pi / 3 ) + i sin 2 pi / 3 ) = 2 e ^2 pi i / 3 } now six root -1 + i roo3 = 2^1/6 e ( 2 pi/3...

Hello everyone, I have just created my account here and so this is my first post and I would like to appologise if my question may have been posted by someone else. I am new to mathematica but I am very found of the program. So much so that I am trying to use it for one of my research...

I've been playing around with a forumlaic representation of a known square roots estimation method and I came up with this: This estimation has several interesting properties to it which I've been looking into. My main concern is the fact that I'm using SQRT(x) in the equation which...

Homework Statement The question wants me to first estimate the roots by drawing the graph and then by using a 'suitable' fixed point method to determine the first 4 positive roots. Homework Equations 0=x-tan (x) I rearranged to get x=arctan (x) so that the series x_n will converge...

So there's this ODE: yy''-(y')2 = y3 After doing some work it gets to this point: (y')2=2y3 Taking the root: y' = +-(2y3)1/2 My question is, what do I do with the +-? Do I solve 2 different integrals? Assume that this is positive? Does it matter if it has starting conditions (y(x)=a...

Show that a complex number, w exists such that the fifth roots may be expressed as 1, w, w^2, w^3 and w^4I am having trouble understanding what the question is asking of me. Could anyone please help? Thanks.

Hello all, I'm attempting to find in literature a method of determining from a Lie algebra's full root system in an arbitrary basis which roots are simple. It seems there are many books, articles, etc on getting all the roots from the simple roots but none that go the other way. My task is...

x^4 + 7x^2 + 6 =0 I know the answers are imaginary but I don't remember how to solve this equation.

Hi there I was wondering if there is a simple way to solve for the roots of a complicated summation of trig functions that can't be combined with any simple identities. I have an equation of the form: 0 = sin(8x-arctan(4/3))+3.2sin(16x+pi/2) where the two sines have different amplitudes...

Homework Statement If x = -1; 1 are the two roots of the equation x^2 +ax+b = 0; then find the values of a and b. The Attempt at a Solution x^2+ax+b=0 (x-1) (x+1)= 0 ,,,,,, by expanding x^2-1=0 ,,,,, so a=0 , b=-1 is it right or the question is asking for something eles,,,, ?

My "Computational World" class is supposedly an intro to computer science without programming, but the questions are all over the place. I'm completely stuck on this question: Show expressions for: (a). 3 cube roots of -1 (b). 4 fourth roots of -1 (c). In the general case, N nth-roots of...

The function y=e^x can be expanded using the power series, thus y=e^x=1+x+\frac{x^2}{2}+\frac{x^3}{3!}+... This is a polynomial of infinite degree, and the theorem that says a polynomial must have at least one root in the complex field, and thus this extends to a polynomial of nth degree having...

Not sure where this should go, but - How would you calculate the square root of a triangular number with a base other than 1? For example, 2, 6, 12, 20 (Base 2). Would rather have help to figure it out than the actual formula.

Homework Statement The equation x4-6x3-73x2+kx+m=0 has two positive roots, \alpha \beta, and two negative roots, \delta \gamma. It is given that \alpha\beta=\delta\gamma=4 (i) Find the values of k and m Homework Equations stated above The Attempt at a Solution m =...

Homework Statement If a and b are positive real numbers, and \lambda^{2} = ab, then \lambda = \pm \sqrt{ab}. Homework Equations None. The Attempt at a Solution This is more of a conceptual question that has always escaped me. I do not understand how the square root of two...

Is there a mathematical equation to find square/cubic/etc. roots of a number? Any help would be greatly appreciated - this is purely for my own interest. Also, I;m doing the C2 module of AS Maths so I may not understand more complex terms used in an explanation (if any are needed) - apologies...

Homework Statement The equation x3 − 3x2 + px + 4 = 0, where p is a constant, has roots α −β , α and α + β , where β > 0. (a) Find the values of α and β . (b) Find the value of p. how do i start off? all i know is that sigma a= -b/a and ab= c/a and ab(gamma) = -d/a . Would this be one of...