Roots Definition and 962 Threads

What are the primitive roots of Z_32? \varphi(\varphi(32))=8 However you must first check that there is a primitive root. A PR exists if (a) n=2,4 (b) n=p^k (c)n=2p^k According to the solutions, Z_32 has no primitive roots. Is this correct? 32=2^5 which fulfills one of the conditions (b) so...

I have some math problems What is the solution to this equation : z dash(complex conjugate) = z^3 Z is complex number I try to multiply both sides by Z in the left i get Z dash Z => |Z| but i don't see the solution ---- P is primitive 9th root of unity. Calculate the sum 1 + 2P...

Homework Statement hello, i am stucked at an article from sciencedirect . somewhere it gives me the following equation and then it tells that this equation must have 4 complex roots! the variable is lambda and we want to find 4 lambda complex roots Homework Equations λ^4=0The Attempt at a...

Is there a formula for finding the roots of a bivariate polynomial in x and y with the form: (a^2)xy+abx+acy+bc Where a, b, and c are constants, of course.

Homework Statement Formulate a conjecture for the equation (z^3)-1=0, (z^4)-1=0 (z^5)-1=0 and prove it. Homework Equations r^n(cosnθ + isinnθ) The Attempt at a Solution Well my conjecture is that 2pi/n and 2pi/n + pi are possible values. I'm a bit iffy on how to word it. don't...

i find it puzzling how to solve this,,. (2)^1/6 or (20)^1/8 without a calculator

hey i'm trying to figure out how to approach part b of this problem, http://imageshack.us/a/img850/6059/asdasdno.jpg so i can see that you can apply the mean value theorem to p'(x) so there exists some c between a and b such that f'(c) = [f(b) - f(a)] / (b-a)=0 so p'(x)...

Question: 1.Find the range of values of \(a\) for which \[(2-3a)x^2+(4-a)x+2=0\]has real roots.2. If the roots of the equation \(4x^3+7x^2-5x-1=0\) are \(\alpha\) , \(\beta\) and \( \gamma\),find the equation whose roots are: (a) \( \alpha+1,\beta+1\) and \(\gamma+1\) (b) \(\alpha^2 \beta^2\)...

Challenge Problem $1,a_1,a_2,a_3, \cdots ,a_{n-1}$ are the $n^{\text{th}}$ roots of unity. Find the value of i) $(1-a_1)(1-a_2)(1-a_3) \cdots (1-a_{n-1})$ ii)$\displaystyle \frac{1}{2-a_1}+\frac{1}{2-a_2}+\frac{1}{2-a_3}+\cdots +\frac{1}{2-a_{n-1}}$

\int\frac{2}{(x+3)\sqrt{x+10}}dx _____________________________________ First thing would be u-substitution, finding what I can replace in terms of u: let u=\sqrt{x+10} \frac{du}{dx}=\frac{1}{2}(x+10)^{\frac{1}{2}-\frac{2}{2}}(x+10)' du=\frac{1}{2\sqrt{x+10}}dx → dx=2\sqrt{x+10}du...

Hello, Please help in solving the four set of problems, i will be very happy explaining comment as really want to understand. The problem will spread to the extent of understanding preduduschey. 1 Problems: The set M, M = {e^(j*2*pi*k/n) , k= 0,1,2...n-1} denotes the set of the nth...

Homework Statement Learning to solve cubic equations without the knowledge of any roots, and the easiest way I found out so far is still time-consuming Homework Equations The equation and attempt is shown in the image below, tell me if its unclear :shy: The Attempt at a Solution...

Homework Statement knowing a,b and c are roots 3x^3-x^2-10x+8=0 show that: 1) 1/a+1/b+1/c=5/4 2)a^2+b^2+c^2=61/9 Homework Equations factor theorem --> (x-a)(x-b)(x-c)The Attempt at a Solution can only use factor theorem: therefore (x-a)(x-b)(x-c)--> up to: x^3-x^2(a+b+c)+x(ac+bc+ab)-abc no...

Is there a method to finding the roots of quartics besides Ferrari's formula? I have the equation x^{4}+5x^{2}+4x+5=0 I know one of the factor is something like $$x^{2}+x+1$$ and the other one can be found using sythetic division, but how can I find the factors without knowing one of...

A linear equation has 1 root A quadratic equation has 2 roots(including two equal roots and two complex roots) A cubic equation has 3 roots Is this means that the no of roots of a equation in one unknown depends on the degree of the polynomial?Why?Any proof and explanation? Thx a lot :)

Hi guys, I'm really new to calculus and limits and have been trying to have a good crack at the following question. Sorry if I haven't written the problem out in the most acceptable format. lim (9-3√x)/(9-x) x→9 Substituting 9 gives you 0/0 and indeterminate. I tried multiplying the...

Homework Statement hi every one I need to construct a C++ square root program that uses approximate values I've done the first part of the work; ********************************************************************************************************************* prompt the user for two...

I observed the following: 1) $\sqrt{2}$ is irrational. 2) $\sqrt{2}+\sqrt{3}$ is irrational(since its square is irrational). 3) $\sqrt{2}+\sqrt{3}+\sqrt{5}$ is irrational(assume its rational and is equal to $r$. Write $r- \sqrt{5}=\sqrt{2} + \sqrt{3}$. Now square both the sides and its...

I am trying to find the z0 to z6 roots of this equation but I am stuck here. Anyone care to show the step by step on how to procced?

Homework Statement 1. z^6=(64,0) 2. z^4=(3,4) Homework Equations These are expanded out into Real and Imaginary components (treat them seperate): 1. REAL (EQ 1) - x^6-15x^4y^2+15x^2y^4-y^6=64 IMAG (EQ 2) - 6x^5y-20x^3y^3+6xy^5=0 From here, you basically solve these for all six...

Homework Statement Let P(z)=1+2z+3z^2+...nz^(n-1). By considering (1-z)P(z) show that all the zeros of P(z) are inside the unit disk Homework Equations None given.. The Attempt at a Solution Well (1-z)P(z) = 1+z+z^2+...+nz^n and to find roots I set it to 0: 1+z+z^2+...+nz^n = 0...

I have the answer to this problem but I am stumped as how to get there. Here it is h(x)=e^x/5/sqrt2x^2-10x+17, I'm getting stuck moving the square root up. Help

Homework Statement Let p be a polynomial. Show that the roots of p' are real if the roots of p are real. Homework Equations The Attempt at a Solution So we start with a root of p', call it r. We want to show that r is real. Judging by the condition given, I am assuming that...

Homework Statement Let x = third root of [root (108) + 10] - trird root of [root (108) - 10]. Show that x ^ 3 +6 x-20 = 0 from which to infer the value of x (is a small natural) The Attempt at a Solution may can i have some ideas how to find this? i tryed to find the x but i don't know...

$y' = \begin{pmatrix}1 & 2\\ 0 & 1\end{pmatrix}y$ The characteristic equation is $$ \lambda^2 - 2\lambda + 1 = (\lambda - 1)^2 = 0. $$ So the eigenvalues are $\lambda_{1,2} = 1$. Solving $(1 - \lambda)y_1 + 2y_2 = 0\iff y_2 = -\dfrac{1}{2}(1 - \lambda)y_1$, we have $$ y = \begin{pmatrix} 1\\...

Hello dear Physics Forums users. I m currently studying some Integrals from a book which my elder brother studied with years ago, and one of the problems had the denominator: x^3-7x+6 Well, I m sure that's over my level, and teacher will never ask this, but in the solution it says its...

Mod note: These posts are orginally from the thread: https://www.physicsforums.com/showthread.php?t=626545 The square root is not defined everywhere, at least not as a function, but as a multifunction, since every complex number has two square roots. I mean, the expression z1/2 is ambiguous...

Hi All I am rusty with my my math and got stumped with a straight forward question regarding vibrations and complex roots. I have a 2nd order ODE x'' +4 x' + 16 x = some forcing funciton This turns out complex roots. I go through the run around of solving this and I get a...

if f(x) is twice differentiable function such that f(a)=0; f(b)=2; f(c)=-1; f(d)=2; f(e)=0, where a<b<c<d<e; then minimum number of zeroes of g(x) = (f'(x))2+f''(x)f(x) in the interval [a,e] is ... All I can figure out is that at the least, it is a 4-degree polynomial with roots a, (b,c) (a...

Let's say that the variable 'x' is definitely some negative number. So if I wanted to solve: x^2 = 4 I get: \pm \sqrt{x^2} = \pm \sqrt{4} \pm x = \pm 2 I would have to take the positive value of 'x' and the negative value of '2' to make this true...is it okay to only take a positive square...

What are the 4 roots of a function y^2 = x^3 + x + 6 (mod 5 * 9^2)? I don't know where to start a problem like this. The roots mod 5 are (0,1) (0,4) (2,1) (2,4) (3,1) (3,4) (4,2) (4,3) if that helps

So there are four square roots for an elliptic curve represented by an equation something like this: y^2 = x^3 + x + 6 (mod 5) How would one go about calculating these?

I'm reading up on some methods to solve differential equations. My textbook states the following: "y_{1} and y_{2} are linearly independent ... since \sigma_{1}-\sigma_2 is not an integer." Where y_{1} and y_{2} are the standard Frobenius series and \sigma_1 and \sigma_2 are the roots of...

Homework Statement Solve the equation: \sqrt[3]{x+1}+\sqrt[3]{x+2}+\sqrt[3]{x+3}=0 The Attempt at a Solution What I did was move (x+3)^(1/3) to the other side, cube both sides and when I put them equal to 0 again, I managed to factor (x+2)^(1/3) out of it giving one solution x=-2...

How do we treat expressions under a sqaure root in inequalities ? Like for ex. x+4< Math.sqrt(-x^2-8x-12) (sorry, using m.physicsforums, so i don't know what to use for a root, so JAVA :p) I request the use of this very example.

Homework Statement Find 5th roots of unity solving algebraically x^5-1=0. Using the result, find sin18 and cos18The Attempt at a Solution x^5 = 1\\ x = \sqrt[5]{1} since we have 5 roots: x_k, k = 0,1,2,3,4 \\ \\ x_k = e^{i\frac{2k\pi}{n}}, n=5 \\ x_0 = e^{i0} = 1\\ x_1 =...

I'd like to know how to find the root of a polynomial on my TI-84 Plus without this "Polynomial Root Finder and Simultaneous Equation Solver" app. The reason is that the app's not in my calculator and I can't transfer the app to my calculator. I keep getting an "Access Denied" error message...

If I see an expression like \sqrt{E^2c^2} I can just remove the square root sign right and replace it with Ec?

Are the roots of a polynomial given by the function f(x) defined as the values for x where f(x)=0? Does that mean f(x)=x^2 has only one root? Even though for every other value of x except zero there are two values for x that you can input to output a particular value for f(x). What about...

Greetings all. I hope it's OK to post here. My issue here is with the theory and not with the actual algebra or calculus. I understand this calculus question on parametric curves except why there must be a double root instead of just a repeated root in the last part. Please see the red...

Hi, I've got an interpolating function which has been generated from using NDSolve and I'm trying to find all the values of x for which the y value is equal to 2. I've constructed a (much) easier example to show what I mean. Suppose I have a set of points which I have generated an...

In a lot of places, I can read that the roots of unity form a cyclic group, however I can find no proofs. Is the reasoning as follows: Let's work in a field of characteristic zero (I think that's necessary). Let's look at the nth roots of unity, i.e. the solutions of x^n - 1. There are n...

Show that the equation x^3-12x-7.2=0 has one positive and two negative roots: I know this can be solved by trial and error, and finding f(0),f(1-4),f(-1 - -4) I have shown that It has two negative roots and one positive however I'm wondering if there is another method on how to show it has...

Ok, to start off I have been examining the structure of polynomials. For instance, consider the general polynomial P(x)=\sum^{n}_{k=0}a_{k}x^{k} (1) Given some polynomial, the coefficients are known. Without the loss of generality...

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...

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...

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...

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.

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)...

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 *...