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

    Partial Fraction Expansion with repeated & complex roots

    I am having trouble to find a straight forward method for finding coefficients using partial fraction expansion with repeated or complex roots. My study notes arent too clear so I am finding the differentiation method hard to follow for repeated roots. As for complex roots I can find the roots...
  2. James889

    Finding Three Cube Roots of -1+i: Exploring Complex Roots in Math

    Hai, I wanted to find the three cube roots of -1+i And since the questions says `three` n = 3 So it should be something like this \sqrt{2}cos(\frac{3\pi}{4} + i sin(\frac{3\pi}{4}) But the key says that the answer is on the form 2^{1/6} why? clearly n was 3?
  3. G

    Second Order Homogeneous Eq's, Auxiliary Eq for complex roots - Help

    Hi I'v got a maths exam on Tuesday for my 2nd year of chemial engineering. Been going through a past paper and have been going over 2nd order homogenous DE's Im at the stage of calculating the roots (wether repeated or 2 distinct roots) I take the easy path like so: E.g m2 + 4m + 4 =...
  4. Porty

    Finding the Value of n for One Root to be the Reciprocal of the Other

    This is probably very easy, but anyway.. I just don't really understand the question, therefore don't know what answer to give.. Homework Statement The question reads... For what values of n will one root of the equation (n - 2)x^2 + (n + 2)x + 2n + 1 = 0 be the reciprocal of the...
  5. J

    How can I find the roots of a cubic equation?

    I've been looking at some practise exams for the University I would like to apply to, I have to sit the exam on 4th November. We have never done finding the roots of a cubic equation before and I cannot figure it out from looking on the internet, the formulas are all horrible to understand...
  6. S

    How Are Negative nth Roots Calculated?

    This has been bugging me for a few days now. Usually when I have a question about math I can answer it myself, but this, the answer is evading me. I know that the answer to the negitive square root of 100 is .1. How is this number obtained? Is there a graphical representation? Does the...
  7. S

    Can You Find a Root of f(x) with Only f(x_1)==y and f ' (x)?

    Is it possible to find a root of f(x), given just f(x_1)==y and f ' (x)? if so, how would one go about it? If this is in the wrong forum can a mod please move it? thanks.
  8. V

    Easy algebra - Calculus question help - find roots of

    1: Which of the following is incorrect a cos2x = 2-(sin^2) x b (sin^2)x + (cos^2)x = 1 c cos x = sin ( pi/2 -x) d sin2x = 2sinxcosx I know b is correct, fairly sure c is correct because i know cos is out of phase by pi/2 have no bloody idea how to determine which of these is...
  9. J

    Derivative of a sum of functions, also cubic graph roots

    Derivative of a sum of functions What would you interperate this as? It is one of the subsections of Differentiation from the syllabus of a University entrance Exam in November but I cannot think what it is referring to. Differentiation: Derivative of xa, including for fractional...
  10. T

    The Origins of i^i=e^(pi/2): Exploring its Mathematical Roots

    could someone tell me where the i^i=e^(pi/2) came from??
  11. J

    Solving Cubic Equations with Chebyshev Roots

    Say I have a monic polynomial, x^3 + ax^2 + bx + c with a=-2.372282, b=1.862273, c=-0.483023 The discriminant is given by a^2 b^2 - 4 b^3 - 4 a^3 c - 27 c^2 + 18 ab c which is < 0, indicating 1 real root and 2 complex conjugates. A method for solving a general cubic using the...
  12. P

    Number Theory integer roots Problem

    I've been stuck on this for a while now, and I was wondering if anyone could help me out. The problem is: If ax^{2}+bx+c=0, prove that all integer roots divide b I'm fairly new to number theory, but this is the one problem that's been really tough for me. If someone could even give me...
  13. J

    Solving cubic roots (with imaginary number)

    Homework Statement (0.1 - 0.3j)^(1/3) = a + bj, where j is the imaginary number or more specifically sqrt(-1). Does anyone know how to solve for a and b? Homework Equations I've looked at cubic function equations, along with some polar equations. However, the latter requires some angle...
  14. Mentallic

    Polynomial Roots Homework: Find 2nd Polynomial with Squared Roots

    Homework Statement Given a general cubic a_1x^3+b_1x^2+c_1x+d_1=0 has roots \alpha,\beta,\gamma find the polynomial a_2x^3+b_2x^2+c_2x+d_2=0 that has roots \alpha ^2,\beta ^2,\gamma ^2 The Attempt at a Solution \alpha ^2+\beta ^2+\gamma...
  15. L

    Mathematica Finding all the roots of a function with Mathematica

    Hi guys and girls of physics forums, 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...
  16. A

    How to solve the equation with square roots

    Homework Statement I am having trouble to find out what rule to use when solving this equation: y=5x^2 square root of (2x^3)/15x^7 square root x How do you right square roots on the keyboard. As you can see I am quit new to this forum Homework Equations I have tried to use the...
  17. V

    Finding Roots of Polynomials in C

    Homework Statement Show the the equation f(z) = z^4 + iz^2 + 2 = 0 has two roots with |z|=1 and two roots with |z|=sqrt(2), without actually solving the equation.Homework Equations Rouche's theorem, the argument principle?The Attempt at a Solution This is what I have done so far: First show...
  18. R

    Algebra - roots of the equation

    Homework Statement If the roots of the equation ax^2+bx+c=0 are α , β and if the roots of the equation a′x^2+b′x+c′=0 are (α +γ) , (β+γ) , prove that : a′^2(b^2-4ac)=a^2+(b′^2-4a′c′) Homework Equations The Attempt at a Solution
  19. E

    Is there a new solution for Cardano's formula?

    Just asking: is it likely that there is any connection between roots as \sqrt[3]{1} and \sqrt[7]{1}?
  20. D

    Finding possible and actual rational roots

    Homework Statement a) 2x^4 - 15x^3 + 23x^2 + 15x - 25 = 0 b) 12x^3 - 20x^2 + 23x - 10 = 0 Homework Equations The Attempt at a Solution I was wondering if you guys could check my answers. For A: Possibles: +/- {1, 5, 25} / {1, 2} Actual: 5, 5/2
  21. F

    Complex Numbers - Finding roots

    Homework Statement Solve the equation z^4= -i Homework Equations De Moivre's Theorem The Attempt at a Solution I understand how to find the roots by equating modulus and argument but I wanted to ask how do you know which arguments to take? Because I got up to 4*theta = -Pi/2...
  22. R

    [complex functions] finding complex roots in 1+z+az^n

    Hi, I have a big problem in solving such question: I have no ideas how to solve it. I thought about integrating W and showing that it's roots create a circle with radius equal to 2, but it completely didnt work. I would appreciate if someone could give me a clue, as I really can't see any...
  23. S

    Proving No Constructible Roots for x^(6) - x^(2) + 2 = 0

    Homework Statement prove that x^(6) - x^(2) +2 =0 has no constructible roots Homework Equations see above The Attempt at a Solution I have to divide the equation by x^(3) which would give me x^(3) - x^(-1) + 2x^(-2)= 0 I can't find a suitable substitution in terms of x which...
  24. P

    Common roots of multivariate polynomials

    I was wondering if it were possible to efficiently solve the common root of 4 polynomials in 4 variables algebraically. I am currently using a gradient descent method, which can find these roots in a couple seconds; however, I am concerned about local minima. So far I have attempted to use...
  25. O

    Simplifying Expressions Involving Square and Fourth Roots

    I was looking over a problem to make sure I hadn't messed up my arithmetic and I put the term (-SQRT(18-12SQRT(2))/6 into my calculator and it reduced it to (2SQRT(3)-SQRT(6))/6. I found approximate values for these two expressions and they were in fact equal. So my question is, how does one...
  26. I

    How do I solve a quadratic equation involving square roots without foiling?

    [b]1. Sqrt(x)+1=-2Sqrt(x-3) 1.) Sqrt(x)=-2Sqrt(x-3)-1 ( )^2 gives 2.) x= (-2sqrt(x-3)-1)^2 and here I think you need to attempt to foil but I am not sure how it works. (-2sqrt(x-3)-1)(-2sqrt(x-3)-1)=x 3.4sqrt(x-3)+2sqrt(x-3)+2sqrt(x-3)+1=x? Not really sure if...
  27. A

    Complex Roots - Not sure I did this right

    Hello. I'm not sure whether I did this right or messed up somewhere, just need to confirm my results...thanks to anybody who bothers answering. Homework Statement Find all the roots of z^{4}=1-i Homework Equations I guess I should state De Moivre's here... (r...
  28. R

    [complex functions] polynomial roots in a convex hull

    Hi everyone, I've got this problem to solve: My problem is that I don't fully understand the question. I have found such definition of convex hull: So I do have to prove, that all the roots of W'(z) [let's denote them as z'_k] must be able to be written in such form: z'_k = \sum_{k=1}^n...
  29. U

    Non-integer roots of complex numbers

    Homework Statement \sqrt[n]{Z} has exactly n distinct value for integer n. What can you say about non-integer n's ? Homework Equations \sqrt[n]{Z}={|Z|}^{1/n}.(cos((\theta+2k\pi)/n)+isin((\theta+2k\pi)/n) The Attempt at a Solution I used Euler's formula to see clearly what the...
  30. V

    Find roots to quintic polynomial

    Homework Statement Find the roots to the polynomial x4+x+1 this is a problem I am stuck with for my algebra class Homework Equations there are a few tricks I have learned for finding roots like taking conjugates and rewriting using fundamental theorem of algebra but we haven't worked...
  31. K

    Finding a value to get certain types of roots

    Homework Statement With what value of g, the roots of s^2+s(1-g)+1 are in the left half-plane (e.g. s=-2 \pm 3i) or single value in the imaginary axis (e.g. s= \pm i) The Attempt at a Solution s= \frac{g-1 \pm \sqrt{g^2-2g-3}}{2}. The roots are complex, if g^2-2g-3<0 \Rightarrow -1<g<3 and...
  32. U

    How to solve a complex equation using quadratic formula

    Homework Statement Find all complex solutions to the following equation: 3(x^2 + y^2) + (x - iy)^2 + 2(x + iy) = 0 Homework Equations I want to use the quadratic formula, but not sure if it applies here. The Attempt at a Solution This is as far as I can get. What I would like is some idea...
  33. B

    Solving z*exp(z)=a: Proving Infinitely Many Roots

    This is not a homework problem, it is something that is stumping a group of us right now. Show that z*exp(z) = a Has infinitely many roots in the complex plane. I would caution against a series approach as we can't guarantee roots of the polynomial z*exp(z) - a. Any ideas?
  34. U

    Simplifying fractions with roots

    Homework Statement Simplify \frac{x^2 - \sqrt{x}}{\sqrt{x^5}} Homework Equations Unsure The Attempt at a Solution Tried to factorise the numerator and denominator. Not sure how to proceed given the subtraction in the numerator. Best effort so far...
  35. G

    Explain the difference between these square roots

    Hey guys, I was just wondering what the difference between these two statements are: V¯(x) = ± 4 V¯(x) = - 4 ---> does not exist. This is the quote from my text, "...we remind you of a very important agreement in mathematics. The square root sign V¯ always means take the positive...
  36. K

    Abstract Algebra - roots of unity

    Homework Statement I want to find out if the sixth root of unity is a subgroup of the complex numbers with multiplication. Homework Equations The Attempt at a Solution I know it's true but my problem is getting there. I know the sixth root of unity must be closed under the...
  37. R

    Solving derivative with roots in denominator

    Homework Statement i have to get f'(x) using the limit definition of the derivative (lim as h approches 0 f(x)= (f(x+h) - f(x)) /h) and I don't know where to start. f(x)= 3/(sqrt(1+x^2) Homework Equations what do I do with the (sqrt(1+x^2) 3. The attempt at a solution I have...
  38. K

    Complex roots of a polynomial

    Homework Statement Let a0 > a1 > a2 > ... > an > 0 be coefficients of a polynomial P(z) = a0 + a1z + a2z2 + ... + anzn. Let z0 be complex number such that P(z0) = 0. Show that |z0| > 1. Homework Equations Triangle inequality? Not sure if that's enough. The Attempt at a Solution I...
  39. T

    How to Isolate Implicit Equations Involving Logs, Sines, and More?

    I was working on double integrals when I came across the equation: x^(3/2)=sin(x). There was no noticeable way to isolate the equation for x without having a function of x equal to x. I am wondering how to isolate equations involving logs, sines, etc when it is given in an implicit form. Using...
  40. wolram

    Ancient Shipbuilding: Prehistoric Roots Revealed

    This was on tv today, it seems to me that boat building could stretch way back into pre history. http://www.sciencenews.org/view/generic/id/39810/title/Shipwrecks_harbor_evidence_of_ancient_sophistication PHILADELPHIA — Surprising insights about ancient shipbuilding have floated to the...
  41. G

    Methods and complexity for computing square roots

    Hello everybody, Let's say we want to compute sqrt(x), where x is an integer of n digits. Then what is the cost of the computation, in terms of big O notation and n? And a second question: what is the algorithm for finding the square root that is most commonly used in computers and...
  42. C

    How can I simplify a nested square roots limit without using l'Hopital's rule?

    Homework Statement Homework Equations The Attempt at a Solution I don't have any idea to simplify the function please help me...
  43. D

    2nd order ode w/complex conjugate roots

    x''+x'+2x=0 x(0)=2 x'(0)=0 I've taken the characteristic equation and reduced the roots to 1/2 +- Sqrt(7/4)i of the form a +- bi (i = sqrt(-1) Then i put the homogeneous solution into the form of e^{}at*(B1cos(bt)+B2sin(bt)) for B1 i used the first i.c. and found that B1=2...
  44. O

    Is e^ix multivalued, roots of unity, etc

    questions: why is the sum of all the roots of unity equal to zero? z^(1/n)=z1,z2,...zn z1+z2+...+zn=0 It's obviously true when there's an even number of roots, (because each root has a partner that is pi radians away and therefore the negative of the other root). but i can't figure out...
  45. S

    Finding Arbitrary nth Roots of -1 Algebraically

    is there a way to find all of the arbitrary nth roots of -1 algebraically?
  46. Mentallic

    Can the Roots of Polynomials Be Proven?

    It is basic knowledge that if a polynomial P(x) of nth degree has a root or zero at P(a), then (x-a) is a factor of the polynomial. However, can this be proved? or is this more of a definition of roots of polynomials?
  47. Mentallic

    Find Polynomial Roots: x^4+2x^3-8x^2-18x-9=0

    Homework Statement If the sum of two roots of: x^4+2x^3-8x^2-18x-9=0 are equal to 0, find the roots of the equation. Homework Equations For this quartic, P(x)=ax^4+bx^3+cx^2+dx+e Let the roots be \alpha, \beta, \gamma, \delta \alpha +\beta +\gamma +\delta=\frac{-b}{a}...
  48. A

    Finding Positive Roots for 2x3-12x2-3x+36=0

    I'm not sure I need to post the whole question, but if I'm having difficulty I will. Basically I'm not sure what the root they are asking me to find is. I have a curve of y=2x2(6-x) and the line y=-3x+36 and I've plotted both of these on a graph. I've shown that where the line and the curve meet...
  49. A

    Building positive roots from simple roots

    Hi, I've got two related questions. You can decompose a (semisimple) lie algebra into root spaces, each of which are 1-dimensional. If X has root a and Y has root b then [X,Y] has root a+b. If the root space of a+b is not zero (i.e. there is a root a+b) then is it possible for [X,Y] to still...
  50. B

    Number of primative roots in finite fields of order p^n

    Is it true as it is for finite fields of order p^1, that the number of primitive roots of fields of order p^n is the euler totient of (P^n-1)? If not is there a different rule for the number?
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