What is Roots: Definition and 976 Discussions

The Roots are an American hip hop band, formed in 1987 by Tariq "Black Thought" Trotter and Ahmir "Questlove" Thompson in Philadelphia, Pennsylvania, United States. The Roots serve as the house band on NBC's The Tonight Show Starring Jimmy Fallon, having served in the same role on Late Night with Jimmy Fallon from 2009 to 2014.
The Roots are known for a jazzy and eclectic approach to hip-hop featuring live musical instruments and the group's work has consistently been met with critical acclaim. ThoughtCo ranked the band #7 on its list of the 25 Best Hip-Hop Groups of All-Time, calling them "Hip-hop's first legitimate band."In addition to the band's music, several members of the Roots are involved in side projects, including record production, acting, and regularly serving as guests on other musicians’ albums and live shows.

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  1. C

    Integrating square roots with trig function and constant inside

    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...
  2. A

    Differential equation: distinct, real roots

    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...
  3. A

    Looking for a software package that finds the roots of complex functions.

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

    Finding Roots of cubic equation

    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...
  5. F

    Complex repeated roots for ODEs

    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...
  6. P

    Solving Complex Number Roots for e^(pi*z)^2 = i | Help Needed

    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...
  7. W

    Solving for the Roots of Z^5 = -1

    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.
  8. T

    Frobenius method indical roots differing by a postive integer

    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...
  9. J

    Mathematica Solving Real Roots with NSolve and Plotting a Bifurcation Diagram

    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!
  10. E

    What is the Number of Complex Roots for the Given Equation with Varying d?

    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
  11. D

    MATLAB-finding roots and summations

    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)...
  12. W

    Are the doppler effects of sound wave and light wave of different roots?

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

    How to solve recurrence relation with one real root and two complex roots ?

    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...
  14. L

    Roots of Lie Algebra (Jones book)

    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...
  15. Telemachus

    Finding the roots through Newtons method

    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...
  16. B

    Check DE general solution with complex roots

    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...
  17. N

    How do roots avoid getting clogged

    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...
  18. D

    Help Getting the roots of a polynomial

    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...
  19. P

    Find All Values of k for Equal Roots in x^2-kx+4=0

    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...
  20. S

    Limit of logarithm of square roots function

    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...
  21. R

    Graphical representation of complex roots to equations

    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...
  22. M

    Roots of Polynomials: Finding g(y) with y1, y2, y3

    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.
  23. P

    Determine the indicated roots of the complex number

    [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
  24. J

    Polynomials: Number of Roots

    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...
  25. R

    Proving the Roots of Higher Derivatives of a Polynomial Function

    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...
  26. S

    What is the Problem with Calculating Roots of a Quartic Equation?

    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...
  27. T

    Integral problems with roots of polynomials

    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
  28. J

    MATLAB Matlab Polynomial Equation Roots Approximations

    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!
  29. sylas

    Greetings from Seoul: Exploring My Korean Roots

    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...
  30. T

    Find Range of k for Two Positive Roots of Equation

    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 ?
  31. I

    Arguments of Roots of Complex Numbers

    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...
  32. M

    Quadratic equation with roots of α and β

    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...
  33. Q

    Unclear situation involving roots.

    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...
  34. B

    What is the Limit of the Product of Roots as n Approaches Infinity?

    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).
  35. S

    Roots of complex function

    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}} ?
  36. J

    Why nth Degree Equations Have n Roots?

    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.
  37. P

    What is the Solution to a Function and Roots Problem?

    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?
  38. S

    Question on ODE's with roots of multiplicity.

    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'...
  39. K

    Numerical Approximation to Roots

    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...
  40. J

    Another repeated roots problem

    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...
  41. C

    MATLAB Exploring MATLAB's Function for Solving Non-Polynomial Equations

    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.
  42. Q

    Second order DE involving repeat roots

    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...
  43. H

    Proving the Three Cube Roots of 1 with w

    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.
  44. r-soy

    Find six distanct sixth roots of -1 + i root 3 I want check my answer

    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...
  45. P

    Mathematica Finding the first roots of a function with Mathematica

    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...
  46. C

    Valid Estimation of Square Roots?

    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...
  47. B

    Fixed point iteration to find the roots of 0=x-tan(x)

    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...
  48. M

    What do I do with the +- in y'= +-(2y^3)^1/2?

    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...
  49. P

    Finding a Complex Number w for Fifth Roots of 1 - Need Help?

    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.
  50. T

    Simple roots of a Lie Group from the full root system

    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...
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