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. J

    Proving roots using mean value theorem

    Prove x^4 + 4x + c = 0 has at most two real roots My thinking is that to prove this I would assume that it has three real roots and look for a contradiction. So I set f(x) = x^4 + 4x + c and assume three real roots x_1, x_2, x_3 such that f(x_1) = f(x_2) = f(x_3) = 0 By MVT I...
  2. B

    Finding Roots and Order of an Integer: Two Problems in Number Theory

    I have two problems I'm working on that I can't figure out. Could anyone please help? 1. show that if p and q are distinct odd primes, then pq is a pseudoprime to the base 2 iff order of 2 modulo p divides (q-1) and order of 2 modulo q divides (p-1) I've been trying this proof by...
  3. B

    Primitive Roots: Exploring Their Significance and Finding Them

    I was curious why primitive roots are so important? Also, how one would find out if a number has a primitive root and what and how many of them they are?
  4. MathematicalPhysicist

    A method to compute roots other than sqrt.

    is there a method to compute roots other than sqrt?, like 10th root or 13th root of a number? and, what are they?
  5. M

    How Do You Find Roots of Complex Polynomial Equations?

    find the four roots of the equation z^4 + 7 -24i = 0 completely lost, some help please...
  6. M

    2 complex roots 2nd ODE, did I mess up finding a constant?

    It is me again, 2 problems later I ran into another problem, I've submitted it a few different times but still is incorrect. Anyone see my mistake? I entered this as the answer: http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/a0/13092fac04d4a01ec22b57e193ed051.png Here is the...
  7. U

    Exploring the 4th Roots of -16

    i am to find the 4th roots of -16 (-16)^{1/4}=2i^{1/4} i=e^{i \pi/2} i^{1/4}=e^{i \pi/8} (-16)^{1/4}=2e^{i \pi/8} or (-16)^{1/4}=2e^{i 5\pi/8} or (-16)^{1/4}=2e^{i 9\pi/8} is this correct?
  8. M

    2nd Order Diff EQ with 2 intial conditions, got complex roots, i f'ed it up

    OKay i havn't gotten 1 2nd order Diff EQ right yet! I'm on a role! wee! Find y as a function of t if 81y'' + 126y' + 79y = 0, y(0) = 2, y'(0) = 9 . Here is my work: http://img204.imageshack.us/img204/4605/lastscan5ag.jpg I submitted this and it was wrong...
  9. M

    Confused on why i'm missing this 2nd Order Diff EQ with complex roots

    Hello everyone. I"m not getting this problem right. <insert sad face here> Find y as a function of t if 6y'' + 33y = 0, y(0) = 8, y'(0) = 5 . y(t) = hokay, here is my work, it is sloppy sorry. Can you see any obvious mistakes I made? Note: the sqraure root should be encompassing both the 11...
  10. L

    Expressing Cube Roots Using Exponential Form e^{i\theta}

    I am asked to use the exponential form e^{i \theta} to express the three cube roots of: (a) 1 (b) i (c) -i what exactly does this question mean? I am really lost as to what they are asking for. here is a stab at it: (a) cube root of 1 is 1... so... would that mean... 1=e^{- \infty...
  11. T

    Understanding Scientific Notation and Exponential Functions

    i'm doing my online homework as we speak and they problem I'm on is this Use your calculator to find the square root of 6.70 × 10^-19 and i calculated that problem in my calculated and i got 6.7e^-19 and i typed it in my homework and its giving me an error and saying "This question...
  12. P

    How to determine the roots of a quadratic equation

    Hello All I am trying to figure out how to determine if there are two, one, zero, or infinitely many roots for given formula ax^2 + bx + c. Are there any easy ways to determine this without having to use the quadratic formula? Thanks P
  13. B

    Roots of Complex Polynomials

    Question that I came across and that has stumped me for about a week hehe. Let p(z)=z^n +i z^{n-1} - 10 if \omega_j are the roots for j=1,2,...,ncompute: \sum_{j=1}^n \omega_j} and \prod_{j=1}^n \omega_j}
  14. T

    Limit of function with square roots

    for sqr root of (n + sqr root (n) ) - sqr root (n),is the answer = zero or infinity so converges or diverges??
  15. M

    What are the solutions to the equation (z+1)^4=1-i?

    find all solutions of the given equation: (z+1)^4=1-i im not sure if i did this right, but here's what i did the first thing that i did was notice that 1-i = 2^1/2 * (cos (pi/4) + i*sin(pi/4)) then i found z= [2^(1/2*1/4) * (cos (pi/4) + i*sin (pi/4) )^1/4] -1 then using de moivre's thrm...
  16. EnumaElish

    Medical Biological roots of passive agressive (PA) personality? PA disorder?

    Does anyone have insights or a perspective on the possible biological roots of PA behavior (or disorder)? I am not a psychologist, psychiatrist, or biologist, but when I think of the evolution of the species it kind of seems obvious that the mammals lived a hard life under the dinosaurs' feet...
  17. L

    Non integer square roots and pi = irrational?

    Since one can construct the length of a non-integer square root by drawing accurate triangles, and can draw a circle with a circumference of pi, then shouldn't one be able to plot corresponding non-integer square roots and pi on a number line? I know these numbers are supposedly irrational, but...
  18. D

    Counting Primitive Roots in Finite Fields without Group Theory

    I have the definition that if F is a finite field then a \in F is a primitive root if ord(a) = |F|-1. Now what I don't understand is how exactly are there \phi(|F|-1) primitive roots? (Note: This material is supposed not to use any group theory.)
  19. A

    Proving Equal Roots in ar^2+br+c=0 with L[e^(rt)]

    If ar^2+br+c=0 has equal roots r1, show that L[e^(rt)]=a(e^(rt))``+b(e^(rt))`+ ce^(rt)=a{(r-r1)^2}e^(rt) could someone offer some advice?
  20. E

    A conjecture about the roots of real functions

    All the roots of a real function f(x) are real unless. 1.K(x) is a Polynomial of degree k 2.f(x)=exp(g(x)) where g(x) is different from ln of something 3.f(z) with z=u+iv is invariant under the transformation of v=-v with f(u+iv)=F(u-iv).. 4.the function f includes some of the functions...
  21. E

    Can a complex potential have real roots?

    Let be the Quantum Potential V(x)=A(x)+iB(x) with A and B real functions then my question is if this potential will have real roots if we take the expected value: E_{n}=<\phi|H|\phi> then the complex part of the energies will come from the expected value <B> so for real energies B should be...
  22. D

    How were logs and roots calculated before calculators?

    I'm not sure whether this is the correct forum, so I apologise if it's in the incorrect forum. Anyway, when studying A level maths a few years ago, we came across a technique for calculating roots that my teacher claimed was used before calculators were invented. I can't remember the actual...
  23. A

    Finding a Basis for O.D.Es with Same Roots

    why is it that when you have the same roots to an O.D.E., you usually add an x or x^2 to get a basis?
  24. J

    Solving Fractions with Roots: an Example

    Hey having a bit of trouble with this question, not sure what to do! QUESTION - express the fraction in the form a + b rootc / d 3 + root24 / 2 + root6 ------------------------------------------ (3 + root24 / 2 + root 6) x (2 - root 6 / 2 - root 6) Simplifying gives (6 -...
  25. 8

    Finding Roots of b1 and b2 Between 0 and 30

    Ok, i got two funktions: b1:=(x/10)+sin((x/3)+(Pi/2)); and b2:=(1-2*cos((x/4)+(Pi/2))); I need to determine all the roots between 0 < x > 30 If I plot the functions i see that there should be two roots plot([b1,b2],x=0..30); But when try to get maple to calculate the roots It only...
  26. U

    Discovering Cubic Root Solutions: A Guide for Scientists

    hello how can i finding roots to cubics?? explain by example :smile:
  27. E

    Are all the roots of an infinite polynomial real?

    let be the function f(x) so we have that if x is a root also x* is a root, but we have that x is NEVER a pure imaginari number,i mean x is always different from x=ia the my question is if this means that all the roots will be real,the only counterexample i find is...
  28. U

    Real find both roots of the equation

    x^2 +6x +k=0 has one root (a) where I am (a) =2, If k is real find both roots of the equation and k So i got b+ 2i is the root (b+2i)^2 +6(x+2i) +k=0 and after expanding it out, i have no clue what to do. Please help. THanks
  29. P

    Find Primitive Root Modulo 125 - The Easier Way

    How would I go about finding a number that is a primitive root modulo 125? There definitely exists a primitive root since 5^3 =125 The problem basically comes down to finding 'a' (primitive root); a^50 congruent to -1 (mod 125) Anyone know a way apart from trial and error? Thanks
  30. M

    Help with finding roots for transfer functions

    I am in a Systems and Vibrations class but am currently doing differential equations. A problem I am doing requires me to find the transfer function [X(s)/F(s)] and compute the characteristic roots. So far I have: X(s)/F(s) = (6s +4)/(s^2+14s+58) That is the transfer function but now...
  31. A

    Sum of Roots of x^3 - mx^2 + nx - 1 = 0

    If m, n, and 1 are non-zero roots of the equation x^3 - mx^2 + nx - 1 = 0, then find the sum of the roots This is what I did.. m, n, 1 are the roots. m and n not equal to 0 x^3 - mx^2 + nx - 1 = 0 f(m) = 0 --> m^3 - m^3 + mn - 1 1 = mn (1) f(1) = 1 - m + n - 1 = 0 ... m = n (2)...
  32. SOS2008

    News The Roots of Terrorism and US Foreign Policy

    In seeing various related topics in PF regarding the reasons for terrorism, solutions for terrorism, the effects of the Bush administration on our country and the world, and more recently nuclear proliferation via the Bush Doctrine, I thought I’d start this new thread, which also may provide...
  33. P

    Primitive Roots: Multiple Possibilities?

    Can a number have more than 1 primitive root? Thanks
  34. E

    Convergence of Nested Square Roots: Solving the Puzzle

    Hi, I came across this puzzle, see if you can solve it :smile: : \sqrt{1 + \sqrt{1 + 2\sqrt{1 + 3\sqrt{...}}}} = ?
  35. E

    A question of roots of riemann function

    let be the quotient: Lim_{x->c}\frac{\zeta(1-x)}{\zeta(x)} where x=c is a root of riemann function... then my question is if that limit is equal to exp(ik) with k any real constant...thanks... the limit is wehn x tends to c bieng c a root of riemann constant
  36. C

    Finding Roots of Complex Polynomials: General Formula and Exponential Form

    Hi all Jut had a question. How do I go about finding the general formula for roots of the complex poly {z}^{n}-a where a is another complex number. Do I just go {z}^{n}=a? :S so complicated this things! Thanks in advance!
  37. E

    Problem with roots of a function h(x)

    Let be the function h(x)=f(x)+g(x) we want to obtain the values of x so h(x)=0 and we have that f(x) and g(x) have the same roots (if a is so f(a)=0 then g(a)=0 too) so we have two types of roots: 1.-values of x that satisfy f(x)=-g(x) 2.values x that make f(x)=g(x)=0 then we make in the...
  38. C

    Roots and complex numbers

    There are n nth roots to every complex number (except zero). My question: How many "roots" are there when you take a complex number to an irrational or transcendental number. For that matter, how do we define raising a number to an irrational number? How do we define raising a number to a...
  39. B

    Equation satisfied by nth roots of unity

    Q. Fix n>= 1. If the nth roots of 1 are w_0,...,w_(n-1), show that they satisfy: \left( {z - \omega _0 } \right)\left( {z - \omega _1 } \right)...\left( {z - \omega _{n - 1} } \right) = z^n - 1 I tried considering z^n = 1. z^n = e^{i2\pi + 2k\pi i} \Rightarrow z =...
  40. A

    Factoring polymonial with complex roots

    This may be a bit silly but i forget how to factor this into complex factors: s^2 + 6s + 25 i know the answer is (s +3 - i4)(s +3 - j4) but how do i get that?
  41. cronxeh

    Auxiliary Equation with Imaginary Roots

    I was curious about what class would cover those types of Linear DE w Constant Coeff, particularly Hyperbolic Functions and exp z type of things. I remember my lecturer said back in Intro DE that we only covered first 2 types of Auxiliary Equations - real distinct roots and real repeated ones...
  42. T

    Complex roots problem (a proof by induction)

    Problem: If c_{1}, ..., c_{n} are the complex roots of a_{n}z^n + a_{n-1}z^{n-1} + ... + a_{1}z + a_{0} = 0 with a_{n} not 0 and S_{k} is the sum of the products of these roots taken k by k, then S_{k} = (-1)^k . \frac{a_{n-k}}{a_{n}}. Prove this by using induction. So for n = 3 this...
  43. L

    How is the distance to the x-axis related to the roots of quadratic equations?

    Hi, How is the roots of a quadratic equation related to the distance from the x-axis at where the root is - where ... ax^2+bx+c=0 and ... x = (-b +- SQRT(b^2-4ac))/2 Can someone help me to establish where this distance relationship to the x-axis and the root come from? Thx! LMA
  44. L

    Proving Odd Number of Real Roots in Cubic Equations

    Hi, A cubic equation has at least one real root. If it has more than one why are there always an odd number of real roots? Why not an even number of real roots? Can someone help me to prove this? Thx! LMA
  45. A

    What is the General Method for Deriving Cubic Roots?

    I've been trying to derive general solutions for cubic roots, i.e. the general solutions of (will Latex just work?) $ax^3+bx^2+cx+d=0$ I do not want to be shown the solutions - but does anyone know what direction to go into achieve this? I thought I'd found solutions at one point but...
  46. E

    Solving Complex Polynomial Equations

    Hi guys, can anyone tell me how I would go about solving this equation? : x^5 = x Rearranging it gives: x^5 - x = 0 But then I don't really know what to do next. I know just from looking at it and thinking about it that the roots should be x = 0, 1, -1, -i, i...but I need to be able to...
  47. H

    Extracting Square Roots in your head

    What are some good quick ways to Extract Square Roots in your head. I'm looking for a method that is very prescice and easy thanks, hopefully somebody helps me out
  48. E

    Finding roots without a calculator?

    hello. I was wanting to know how to raise a number to any power without using a calculator. More specifically, I was wanting to raise numbers to the .5 power, (and all the other roots, 1/2, 1/3, 1/4). How can this be done? <----------------------> My fellow 633|<5 :rofl:
  49. A

    Primitive roots, specifically of 18

    this problem is annoying. I've found that the primitive roots of 9 are 2 and 5. since 2|18 it can't be a root. i know via some theorems in my book that if 5 is a primitive root of 3, then its a primitive root of 3^k, and also of 2*3^k. sorry about not using latex, shouldn't need it for...
  50. A

    Solve another trig eqn with square roots

    solve \sqrt2 \sin\theta= \sqrt3-\cos\theta algebraically for the domain 0<theta<2pi I know that the cos can be changed into 1-sin^2 theta but I don't know what to do after how do I get everything on the right hand side and simplify it?
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