Roots Definition and 962 Threads

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...

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...

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...

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...

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...

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...

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

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

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

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...

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...

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...

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...

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...

[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...

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...

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...

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...

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...

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...

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...

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?

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...

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...

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...

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...

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...

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...

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...

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...

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

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...

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...

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

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?

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}...

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...

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...

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?

Homework Statement I am looking for the fifth roots of unity, which I believe come in the form of: cos(2kpi/5) + isin(2kpi/5), k=1,2,3,4,5 and when k=5, the complex number is 1. how do you convert the rest to complex numbers? Normally, I use common triangles like: 45-45-90 and...

Homework Statement The equation of a curve is y=\frac{3x}{\sqrt{1+x}}. Given that the equation of the tangent to the curve at the point x=3 us 15x-16y=k , find the value of k. [SIZE="5"]SOLVED Homework Equations The Attempt at a Solution

Homework Statement show that the equation x^4+x^3-4x^2-1=0 Homework Equations The Attempt at a Solution I wasn't sure where to start. The minus one at the end really threw me off. I tried to factor by grouping by coul;dn't figure out what to do with the -1

Homework Statement Given an nth order linear homog. diff eq. how can I find the solution for its nth degree characteristic eq? I know its simple Algebra but please help. if possible please give a 5th deg eq. thx

Homework Statement lim (root*(6-x) -2)/(root*(3-x)-1) x->2 Homework Equations i know in a normal limit if a square root was on the top of bottom, you would multiply it and so on so on...but the fact that there is a square root on the top and the bottom is throwing me off...

Homework Statement Suppose 'a' and 'b' are real numbers such that the roots of the cubic equation ax^3-x^2+bx-1=0 are all positive real numbers. Prove that: i) 0<3ab<=1 ii) b>= 3^0.5 Homework Equations Let x,y,z be the roots: x+y+z=1/a xy+yz+zx=b/a xyz=1/a The Attempt at a...

Homework Statement determine the number of roots, counting multiplicities, of the equation z^7-5*z^3+12=0 in side the annulus 1<=|z|<2 Homework Equations use rouche's theorem The Attempt at a Solution

Homework Statement find the roots of: 3x^2 − 4x + 2 = 0 Homework Equations quadratic equation The Attempt at a Solution 4+/- sqrt16-24/6 4+/-sqrt-8/6 4+/- isqrt4 sqrt2 4+/-2isqrt2/6 simplify a bit x= 2-2sqrt2i x= 2+2sqrt2i does this seem right?

Homework Statement how do i find the roots of this: x^2-(2-1)x+(3-i)=0 Homework Equations -b+-sqrtb^2-4ac/2a (quardaric equation) The Attempt at a Solution

Can someone help me use L'HOP to determine lim x -> 0 [ \sqrt{x}*ln(x) ] ? I'm confused!

im trying to work out how to use partial fractions on a fraction with repeated roots. I am learning about laplace transforms at the moment, i don't remeber the lecturer specifically going through how to solve the transforms that have repeated roots and can't find it anywhere in the lecture...