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. Sudharaka

    MHB Common roots and finding real values

    srirahulan's question titled "Algeb" from Math Help Forum, Hi srirahulan, Let \(\alpha\mbox{ and }\beta\) be the two roots of these quadratic equations. Then, according to the first equation, \[\alpha+\beta=-\frac{2}{a}~~~~~~(1)\] Considering the second equation...
  2. J

    Connection between roots of polynomials of degree n

    Homework Statement The two polynomial eqns have the same coefficients, if switched order: a_0 x_n+ a_1 x_n-1 + a_2 x_n-2 + … + a_n-2 x_2 + a_n-1 x + a_n = 0 …….(1) a_n x_n+ a_n-1 x_n-1 + a_n-2 x_n-2 + … + a_2 x_2 + a_1 x + a_0 = 0 …….(2) what is the connection between the roots of...
  3. M

    Can You Find a Number n with Rational Square Roots for n-7, n, and n+7?

    Hi, I am struggling with this puzzle from a book. Puzzle : Can you find a number n such that, the numbers n-7, n, and n+7 have rational square roots (can be expressed as integers or fractions)? According to the book one of the solutions is n =113569 /14400 This is what I have done so...
  4. A

    A quesion on establishment of nature of roots

    we are given an equation x5+x=10 . How to prove that the only root for the equation is irrational? I'm an average 12th standard student. So, please keep it low. Thanks in advance.
  5. 3

    Roots of -8: Solving with Exponential Form

    Homework Statement I'm supposed to find the 6 roots of -8 + 0i we are told the usual method of for these problems is to put the complex number into it's exponential form like so z = |z|exp( i(θ+2πk)) where k: [0 to n-1] then put it to the relevant power 'n' z1/n = |z|1/nexp(( i(θ+2πk)/n)...
  6. AnTiFreeze3

    How do I simplify cubed roots with multiple variables and coefficients?

    Homework Statement Simplify...Homework Equations Starting Equation: ³√9xy^4 * ³√12x³yThe Attempt at a Solution (Sorry ahead of time if this is sloppy) ³√9xy^4 * ³√12x³y - I broke up each part of the cubed roots to try and simplify them³√9 * ³√x * ³√y * ³√y³ * ³√y * ³√12 *...
  7. Saitama

    What is the number and position of real roots of x4+4x3-4x-13=0?

    Homework Statement Find the number and position of real roots of x4+4x3-4x-13=0. Homework Equations The Attempt at a Solution I found the number of real roots using the Descarte's rule of signs. One is positive and other is negative. Now about the position of roots, i don't have...
  8. H

    Calculators How do I calculate roots with the 15c

    I'm trying to calculate the cube root of -8, for example, so I type in these buttons: 8 CHS (change sign) Enter 3 1/x y^x But it gives me an error. What is the correct way to go about doing this?
  9. S

    Kronecker's theorem - Find a field with roots for X^4 + 1

    Homework Statement Consider X^4 + 1 in the field \mathbb{Q} [X] . I used Kronecker's theorem to find a root for X^4 + 1 in the field extension \mathbb{Q} [\frac{(1+i)}{\sqrt{2}}] . I'm asked to show that this field extension allows X^4 + 1 to be factorised completely, thus adding a single...
  10. C

    Find sum of roots of polynomial

    How would I go about approaching this problem? Given the polynomial: x^100 - 3x + 2 = 0 Find the sum 1 + x + x^2 + ... + x^99 for each possible value of x.
  11. J

    MHB Roots of a polynomial with non-real coefficients.

    Let a,b,c,d be real numbers. Sauppose that all the roots of the equation $z^4 + az^3 + bz^2 + cz + d = 0$ are complex numbers lying on the circle $\mid z\mid = 1$ in the complex plane. The sum of the reciprocals of the roots is necessarily: options a) a b) b c) -c d) d ---------- Post...
  12. C

    Ambiguity about roots of unity in discrete Fourier transform

    Hi everyone, I have a question on the discrete Fourier transform. I already know its a change of basis operator on C^N between the usual orthonormal basis and the "Fourier" basis, which are vectors consisting of powers of the N roots of unity. But if i recall correctly from complex...
  13. C

    Plotting the roots of unity on the complex plane

    Homework Statement Find the 6th complex roots of √3 + i. Homework Equations z^6=2(cos(π/6)+isin(π/6)) r^6=2, r=2^1/6 6θ=π/6+2kπ, θ=π/36+kπ/3 The Attempt at a Solution When k=0, z = 2^1/6(cos(π/36)+isin(π/36)), When k=1, z = 2^1/6(cos(13π/36)+isin(13π/36)), When k=2, z =...
  14. L

    Galois Groups of Extensions by Roots of Unity

    Consider field extensions of the form Q(u) where Q is the field of rational numbers and u=e^{\frac{2\pi i}{n}}, the principal nth root of unity. For what values of n is the Galois group of Q(u) over Q cyclic? It seems to at least hold when n is prime or twice an odd prime, but what else...
  15. C

    How to find the intersection of complex roots, Im(z) and Re(z)?

    Homework Statement (a) Find the 6th complex roots of √3 + i. (b) Let A={z|z^6 =√3+i} and B={z|Im(z)>0} and C={z|Re(z)>0}. Find A ∩ B ∩ C. Homework Equations z^6=2(cos(π/6)+isin(π/6)) r^6=2, r=2^1/6 6θ=π/6+2kπ, θ=π/36+kπ/3 The Attempt at a Solution I've done part (a): When k=0, z =...
  16. M

    Why do we care so much about the roots of equations?

    Hi, I know what roots are and how to find them but I don’t know why they are so important. What is that makes the points where a function become zero so important? I saw a similar post on this topic, but it talks about roots from an optimization point of view. However, finding roots...
  17. E

    Proving Rational Roots and Irrationality of \sqrt{2}

    Homework Statement Prove that a rational root of a monic polynomial is an integer. Use this to prove that the \sqrt{2} is irrational. Homework Equations The Attempt at a Solution /// I am really not sure where to begin?
  18. C

    MHB Number of real roots of a quartic

    rayman's question from another place: Descartes rule of signs tells you this has exactly 1 positive root, and exactly 1 negative root, so it has two real roots. CB
  19. H

    Cubic polynomial function with 3 real roots; one at infinity?

    Is it possible to have a cubic polynomial (ax^3+bx^2+cx+d) which has three REAL roots, with one of them being +/- infinity? If there is, can you give an example? Thanks!
  20. E

    Maths - a proof question on the nature of roots of quadratic equations

    I'm sorry, I just realized I put this in the wrong subsection. While I figure out how to fix that, please have a look anyway. __ Homework Statement Given x \inℝ And s =\frac{4(x^{2}) + 3}{2x-1} Prove that s^{2} -4s - 12 ≥ 0 Homework Equations The discriminant Δ, (in order for which to be...
  21. N

    MHB Rational roots, functions, modeling.

    OKAY I have a trg test make up and due tomroow and I have no clue what I am doing, I've searched online chatrooms and they all want money. so this is basiaclly my last hope the test is over rATIONAL ROOTS ZEROS POLYNOMIALS ETC. please show all work if answering QUESTIONS i NEED HELP ON BELOW...
  22. naima

    Length of roots in su(2) su(3) and other Lie algebras.

    Hi all I found these equalities from Gordon Brown (1963). He uses the killing form to measure the length of the roots in a semi simple algebra. First and second equalities are quite obvious and come from the definition. Could you help me for the last one which prove that we have a...
  23. C

    Finding the nth roots of a complex number

    Homework Statement find the sixth roots of i. Homework Equations The Attempt at a Solution So I started by Arg(z)=pi/2 and |z|=1=r n=6 so z= r^(1/6)*e^i((5kpi)/12) for k=0,1,2...n-1 and that's as far as I got and there answer = e^i*n*pi/12 for n=...
  24. T

    If z is one of the roots of unity with index n, find the sum

    Homework Statement Given the fact that z is one of the n-th roots of unity, find the sum below: 1 + 2z + 3z2 + ... + nzn-1Homework Equations (1-x)(1+x+...+xn-1) = 1 - xn The Attempt at a Solution honestly I don't know how to do this. any help is appreciated
  25. Q

    Integrating Square Roots - Absolute Value Needed?

    Homework Statement http://i.minus.com/i61zvy2BbtqkI.png Homework Equations One can factor the polynomial to (x-1)^2 The Attempt at a Solution After factoring the polynomial, I integrate (x-1) given the bounds of 0 and 1. I get -1/2. The solution manual says the answer is...
  26. P

    Solve the Equation getting rid of square roots

    Solve the Equation... getting rid of square roots PLZ 1+ √((1+x)√(x^2-24)) = x (x*√(x^2-24)) = (x-1)^2 (Square both side) (-1)+1+(x^√(x^2-24) = (x^2 - 2x +1)-1 x^2(x^2-24) = (x^2 -2x)^2 (Square both sides) x^4 -24x^2 = (x^2 - 2x)^2 x^4 -24x = x^4 - 4x^3 +4x^2 0 = -4x^3 +4x^2 +4x^2 0 =...
  27. B

    Roots of a polynomial and differenciaton

    Homework Statement I read that if f'(x) is zero once in [a b] then f(x) has maximum two real roots. Why maximum? Shouldn't it be exactly 2? Or it has something to do with the case of repeated roots? Homework Equations The Attempt at a Solution was thinking as in figure
  28. S

    MHB Repeated roots, non homogeneous - second order, reduction of order method

    I semi understand the reduction of order method, and i understand the general solution for a 2nd order with repeated roots. however, i can't seem to form up the correct thing to solve this question, and research again proves futile. Any assistance will be appreciated. Use the method of...
  29. D

    Proof of x^3+a^2x+b^2=0 roots question

    I want to prove x^3 + a^2x + b^2 = 0 has one negative and two imaginary roots if b \not= 0. I know that it cannot have any positive real roots because a > 0 and b > 0 will always be the case. I believe I can prove this using Descarte's Rule of Signs (which is in the same chapter of this...
  30. J

    Roots of polynomials over GF(p)

    If F is a field of characteristic p, with prime subfield K = GF(p) and u in F is a root of f(x) (over K), then u^p is a root of f(x). Now, I know that x^p \equiv x (\text{mod } p), so isn't it immediately true that f(x^p)=f(x) (over K)? So, 0=f(u)=f(u^p) . I only ask because this type...
  31. T

    Sum of Squares of Roots of quadratic equations.

    1. The problem: Find the value of \lambda for which the sum of squares of the roots of the equation: 2x^2 + (2\lambda +4)x^2-(1+ \lambda) = 0 has minimum value. 2. Homework Equations \alpha + \beta = -b/a \alpha\beta = c/a where a,b,c are coefficients of x^2 , x and constant...
  32. H

    Roots and Weights in Lie algebras

    Hello! I am trying to understand this subject but its not simple.. I will ask some question but if anybody wants to write a short introduction which explains my confusions in a continiuous text, that would be awesome as well. :) I think I got a good view of what our weigts are.. just...
  33. O

    MHB Real double roots question

    can you look this question and help me? http://img252.imageshack.us/img252/2720/59248444.png
  34. L

    A general condition on polynomial roots

    Consider a polynomial of the following type: A_n w^n + A_{n-1} w^{n-1}k + A_{n-2} w^{n-2} k^2 + ... + A_1 k^n =0 What are the general conditions on {A_i} in order for the roots w(k) to be EITHER real OR functions with even imaginary parts, Im[w[k]]=Im[w[-k]]? I would be interested in...
  35. H

    Roots of a third degree polynomal equation (complex numbers)

    Hey everyone! Here I have a problem I don't know how to solve so help would be greatly appreciated! Homework Statement Here is an equation z^3+az^2+bz+c where a, b and c are real numbers. If the roots are drawn in the complex plane they form a triangle with area of 9 units. One root of the...
  36. A

    Help solving a second order ODE with repeated roots,

    Help solving a second order ODE with repeated roots, urgent! I have a differential equaition d2y/dx2 - 6dy/dx + 9y = 0 I have found the general solution to be y = (Ax + B)e3x Now I need to find the solutions to A and B so that... when y = 4, x = 0 when y = 49.e15, x = 5 I...
  37. M

    Limits with sine and square roots

    Homework Statement solve the limit: \lim_{x\rightarrow1}\frac{sin(x-1)}{\sqrt{x}-1} The Attempt at a Solution Is there a way of how i can solve this without using l'hospital's rule or taylor series?
  38. N

    Roots of a cubic polynomial

    Homework Statement Hello there! I'm trying to find the roots of the following cubic polynomial x^3 - 10x + 18 = 0 The Attempt at a Solution I did the following: I rewrite 18 as 18 = - (x^3 - 10x) then I did back substitution and factored out x^3 - 10x - x^3 + 10x = 0 or x(x^2-10) -...
  39. T

    Finding Multiple Roots of Equations

    Homework Statement Hello everyone. My task is to find the largest positive root in a specific interval of a function using the bisection method, Newton-Raphson method, and secant method. I've written code for all three of these methods, but the only way I can find all of the roots is to hard...
  40. T

    Finding Multiple Roots of Equations

    Homework Statement Hello everyone. My task is to find the largest positive root in a specific interval of a function using the bisection method, Newton-Raphson method, and secant method. I've written code for all three of these methods, but the only way I can find all of the roots is to hard...
  41. J

    Solve Un Subseteq U2n | Roots of Unity Proof

    Hey everyone! I would really appreciate some help with this problem. I have been racking my brain for hours now, and nothing seems to work/convince me. Homework Statement Show that Un \subseteq U2n for every positive integer, n. Homework Equations [1] Un = {z ε ℂ, zn = 1} [2] Un =...
  42. C

    MATLAB MATLAB: Using Roots to Find When Aircraft are 30 Miles Apart

    "roots" command in MATLAB Hey everyone. I'm a new user to Matlab. I must say, it's an awesome program, but not user-friendly at all. I'm having trouble trying to use the "roots" functon. Here's what part b of my problem states: "Use the roots function to compute the time when the aircraft...
  43. P

    Complex Variables (Finding complex roots)

    Homework Statement Find all solutions to (z2+1)2=-1 The Attempt at a Solution I know that because it is a polynomial of degree 4 it is a square inscribed inside of a circle in the complex plane. All i really need is one solution and from that finding the other three is easy. I have tried...
  44. S

    How to solve a cubic equation with two variables and one constant

    Homework Statement SOLVE: √(X)-3√(X-1)=1 //That is SQRT(X)-CBRT(X-1)=1; where SQRT = Square root, and CBRT = Cube root. Homework Equations None that I know of... The Attempt at a Solution (I would like to note I have no idea whether I am even approaching this problem the...
  45. J

    Show that the four of the five roots of

    Show that the four of the five roots of ... Homework Statement Show that four of the five roots of z5 + 15z + 1 = 0 belong to the annulus {z: 3/2 < |z| < 2}. Homework Equations Argument Principle (presumably) The Attempt at a Solution Since f(z) = z5 + 15z + 1 is entire, it has...
  46. D

    Complex Number equations from roots

    Homework Statement Determine the only real values a, b, c, and d such that the equation: z4+az3+bz2+cz+d = 0 has both z1 and z2 as roots. z1 = 3 + j z2 = -5 + 5j Homework Equations z = x + yj. z = |z|ej\theta The Attempt at a Solution I am not sure where to begin. I can...
  47. E

    How to find function with given roots and point

    Homework Statement Find the quadratic function which has x-intercepts -2 and 2 and passes through the point (0,8). I am struggling with solving this one. I tried to substitute values into ax^2+bx+c=y but there are too many unknowns. Can anyone give some tips how to solve it?
  48. T

    Help Finding Roots of Polynomial

    Homework Statement First find all rational zeros of f, then use the depressed equation to find all roots of the equation f(x) = 0. f(x) = x^3 + 5x^2 - 8x + 2Homework Equations The Attempt at a Solution Possible rational zeros: 2, -2, 1, -1 Synthetic division: 1 | 1 5 -8 2 _____1 6 -2...
  49. S

    Partial Fractions (Laplace Transform, complex roots)

    Hello all, Say one wants to find the inverse Laplace Transform of a function, and the method for attaining the solution is executed via partial fractions. Do the real numbers go with the complex numbers when determining the constants of partials? Perhaps this is wordy. I'll provide a theoretical...
  50. A

    Relationship between roots and coefficients

    Homework Statement Homework Equations Sum of roots taken one at a time is -b/a Sum of roots taken two at a time is c/a three at a time is -d/a four at a time is e/a The Attempt at a Solution I did part one by solving the two equations...
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