Roots Definition and 978 Threads

Hi so I am new to calculus and need help with differentiation The question is: Differentiate the following function: sqrt(x^2-8x+20) So far I have gotten =(x^2-8x+20)^(1/2) =(1/2)(x^2-8x+20)^(-1/2) * 2x-8 I am unsure where to go from here I know we are supposed to use the chain...

y=1/squareroot(x+1) y=x Sketch the two graphs, and indicate on your graph the location of the root r of the equation 1/squareroot(x+1)=x. Use algebra and show that x=r can also solve the equation x^3+x^2=1. Calculate r to 5 significant figurees using simple iteration. Im stuck in the...

Homework Statement ∫√(2+cos3(t)) dtI should perhaps have tried to get the lower and upper limits of this integral (it's defined), but all I'm wondering about is how to calculate the integral. I don't need the answer, but if someone could just point me in the right direction. I've tried...

Homework Statement Find the general solution by using either the "distinct, real roots" theorem or the "repeated roots" theorem. 9y'' - 12y' + 4y = 0 Homework Equations "distinct, real roots" theorem - "If our roots are real & distinct, we should have solutions y1=er1x and y2=erxx, so...

Hi, As the title says I'm looking for a software package that computes the roots of complex functions. Thanks.

Homework Statement Consider the motion of particle moving on the inside surface of a smooth cone of half-angle α, subject to the gravitational force. Although this problem does not involve a central force, certain aspects of the motion are the same as for a central-force motion. Show that the...

I know that a 2nd order homo ordinary differential equation's solution is in the form of \[f(x) = {C_1}{e^{{a}t}} + {C_2}t{e^{{a}t}}\] for repeated real roots of the characteristic equation, and that the solution for a single complex root (and its conjugate) involves a cosine. I'm curious...

Hi out there peps, very nice forum! (my first topic) Atm I am dealing with complex numbers, and I've got kinda problem solving this task. Hope for some help. Anyway, it sounds like this. - Name all the roots for the equation e^((pi*z)^2)=i, for which modulus is less than 1. Its...

Homework Statement Z^5 = -1 What are the five roots? Homework Equations The Attempt at a Solution I do not know how to start this problem. I am given a hint to put -1 into the form Ae^(i*delta), but I am unsure as to how I can do that. Any help would be much appreciated.

Homework Statement For what values of the constant K does the differential equation y"-(1/4 +K/x)y=0 (0<X< infinity) have a nontrival solution vanishing at x=0 and x= infinity ? Homework Equations Hints that were suggested for my prof were: For large x...

Hi, I'm using NSolve in Mathematica but I only want to find the roots that are real numbers as my answer gives a lot of imaginary numbers. How can I do this? I want to then plot a birfucation diagram using a table of data. Is there a function to do this? Thanks!

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 I'm trying to find a root-finding method for a function [tex] f: \mathbb R^n \to \mathbb R [/itex] Homework Equations x is a root of f(x) if f(x) = 0 The Attempt at a Solution There is lots of work done for this problem when n=1, and also lots of work done when...

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...