Roots Definition and 978 Threads

Homework Statement Let f(x) be a pllynomial of degree n, an odd positive integer, and has monotonic behaviour then the number of real roots of the equation f(x)+ f(2x) + f(3x)...+ f(nx)= n(n+1)/2 Homework Equations The Attempt at a Solution This seems like the summation of...

Homework Statement How do I find the roots of 4x^3+x+5 = 0? It doesn't appear to be in a nice form like many equations in the textbook?

Hi. I only just recently found out about an algorithm for calculating the square roots of a number. Lets say i want to evaluate \sqrt {n}. I can make an approximation by inspection, and say \sqrt n \approx \frac{a}{b}. Now, using this approximation, i can write: \left[...

1.Solve the following initial value problem d^2y/dt^2 + 4y = { 1, 0<= t <=Pi/2 } {sin(t), Pi/2 < t} y(0) = 2 y'(0) = -1 I used y(t) = e^rt 3. For y'' + 4y' =1 y(t)= e^rt Yp(0)=1 r^2+4 = 0 r = 2i y1(t) = C1 Cos(2t) +...

Homework Statement I need to find the real and imaginary roots of z^4 = -1. The Attempt at a Solution The polar coordinates of -1 are at (-1, pi), (-1, 3pi) etc so if I assume the solutions take the form z = exp[i n theta] then n theta = pi + 2npi This dosen't seem to give the...

Homework Statement Heres the question I'm tackling: <b> the height of a prism is x-1, width x-2, length x+3 and the volume is 42cm cubed. Find the dimensions</b> Homework Equations Quadratic formula, common factor, family of functions The Attempt at a Solution I know that 7, 2...

I want to show that every polynomial of degree 1, 2 and 4 in Z_2[x] has a root in Z_2[x]/(x^4+x+1). Any ideas? Ps. How can I use latex commands in my posts?

can a non-factorable function has rational real roots?

Homework Statement Find all roots of the equation cos(z)=2 (z is a complex number)Homework Equations The Attempt at a Solution What do they mean find the roots of this equation? We're just going over trig functions and it doesn't say anything about roots so I'm not sure what they're...

I'm having trouble following one step in a proof I'm studying. I'm sure I'm missing something obvious, but I just can't get it to work out (it supposed to be "obvious" which is why they left out the details). Anyway, it's part of a proof showing that if you have a monic polynomial with all...

Hi all, is there a general way of proving that sqrt(r1) + sqrt(r2) + sqrt(r3) + ... + sqrt(rn) is irrational, given that none of r1, r2, r3, ..., rn is the square of a rational number? (or is this statement even true in general?) for the case when n = 2, the proof is quite...

Homework Statement Show that for negative c (a,b,c - real) equation x^3+ax^2+bx+c=0 has at least one positive root. 2. The attempt at a solution Considering the equivalent form of the equation above for large |x|: x^3(1+\frac{a}{x}+\frac{b}{x^2}+\frac{c}{x^3})=0 we can conclude that there...

Homework Statement Find all the roots of sin h(z) = 1/2 2. The attempt at a solution sin h(z) = [1/2](e^z - e^-z) = 1/2 => e^z -e^-z = 1 => e^2z - e^z - 1 = 0 {multiplied e^z bothsides} this is a quadratic equation in e^z using quadratic formula, e^z = [1+- sqrt(5)]/2 taking 'ln' on...

Is there a website that given the coefficients of a order 4 polynom, it will give me all 4 roots of this polynom? Thanks.

w_{n} is primitive root of unity of order n, w_{m} is primitive root of unity of order m, all primitve roots of unity of order n are roots of Cyclotomic polynomials phi_{n}(x) which is a minimal polynomial of all primitive roots of unity of order n , similarly, phi_{m}(y) is a minimal...

Need Assistance w/ existence of conjugate roots in polynomial Prove: given that f(x) = Anx^n + An-1X^n-1+ ...A1X + A0 , and An does not = 0 => if f(x) has a root of the form (A+Bi), then it must have a root of the form (A-iB). (complex roots) So far I've come up with the conjugate roots...

All right, thanks to everybody's help, I've got the algorithm for determining the nth roots of unity. However, for determining which ones are primitive, I'm still having a little trouble. If n is odd, I can test if (n, k) are coprime. However, for even values of n, it seems that it doesn't...

Hi eveveryone I was just hoping for some quick help on frustrating physics related math problem. I won't go into detail on the actual problem becasue i know i found the correct polynomial but i was wondering if there was any easy way to find the roots to this polynomial...

(*)p(x) = x^4 + ax^3 + bx^ 2 + ax + 1 = 0 where a,b \in \mathbb{C} I would like to prove that a complex number x makes (*) true iff s = x + x^{-1} is a root of the Q(s) = s^2 + as + (b-2) I see that that Q(x + x^{-1}) = \frac{p(x)}{x^2} Then to prove the above do I then show...

Where can all the classic papers by the experimentalists that layed the foundation for nuclear physics be found?:confused: Rutherford, joliot-curie, fermi, lawrence, Hahn ect. Im very interested in reading exactly how they setup there experiments, the conclusions they drew and so on.

For the function ## y=f(x) ## is there a test to prove if its roots are real or either has some complex roots?, or in more general cases: ## y=g(x)D^{k}f(x) ## k>0 and a real D=d/dx number.:rolleyes: :rolleyes: The question is that sometimes it can be very deceiving to tell if a function...

of the equation z= exp(-z) could someone possibly point me in the right direction to start this problem? this area of math is still new to me so please go easy thanks

I just have two questions: A fundamental problem in crystallography is the determination of the packing fraction of a crystal lattice, which is the fraction of space occupied by the atoms in the lattice, assuming that the atoms are hard spheres. When the lattice contains exactly two...

hi, is there any way to find the cube roots of a complex number WITHOUT converting it into the polar form? i am asking this because we can find the square root of a complex number without converting it. i was just wondering whether there is such a method for finding cube roots too. i was...

Prove that the sum of the roots and product of the roots of the equation ax^2 + bx + c = 0 are -b/a and c/a respectively thank you

Question: How many real roots does the equation x^5 + x + c = 0 have on the interval of [-1,1]? I try to differentiate the equation, then I obtain 5x^4 + 1. When at its local minimum or local maximum, 5x^4 + 1 = 0. So, there is no solution for the equation, since 5x^4 + 1 > or = 1...

The Roots and degree of a polynomial function are given. Write the function in standard form. b) 2, -2i, degree 4 obviously i know there is a function with x^4 and it should have 4 x answers so I don't know how to do this...I know that (x-2) is a factor

the book asks to fnd the four roots of z to the fourth power + 4 = 0 and then use to demonstrate that z to the fourth power + 4 can be factored into two quadratics with real coefficinets. I am clueless on where to start. Please help.

I just bombed a quiz because it was 2 questions and this was one of them: Find all three complex roots of the following equation (give answers in polar and rectangular form) z^3+8=0 Looks easy enough, z=2e^{-i\frac{\theta}{3}} This is where I think I completely realized I wasn't sure what...

I have a feeling the answer to my question is pretty simple, but I couldn't come up with an answer, so I'm going to ask it here. Say you have an equation which looks like this: y^2 = x + 4 Assuming you want to rearrange the equation to solve for y, you would do this: y = square...

How to solve cube roots question ? Example : x^3 - 100x^2 - 7800x + 16300 = 0 I had think long time but still cannot find the way. Besides trial an error, is there anyway to solve this problem ? thank you.

I am stuck half way in solving this problem (the square root nominator confuses me) :confused: : http://img235.imageshack.us/img235/8459/1mi1.jpg and I cannot get it to match the answer given on the back of the textbook: http://img235.imageshack.us/img235/7041/answerop5.jpg Please...

Now this bugs me. First there were no negative numbers. Then there were no square roots to negative numbers. Then every real number had two square roots, but no word on imaginary numbers. Luckily for me, I had a calculator that told me the square root of i wasn't some other type of number or I...

Is there a way to find the,"Sum of the square roots of the first n natural numbers"?

i wonder if there's a formula like for quadartic and cubic equations also for roots polynomials, like this equation: ax^(1/2)+bx+c=0 or like ax^(1/3)+bx^(1/2)+cx+d=0 ? and what are they?

there is a way of calculating the square root of any number (without using a calculator of course). is there a similar way, or any way, in fact to calculate cube roots, fourth roots, etc. again without using a calculator??

for x^2 +4x +5=0 ,may i know how to compute the roots incomplex form?? the answer is -2+j and -2-j thanx

http://album6.snapandshare.com/3936/45466/776941.jpg PS. Just wanted to say thanks for all the help so far. This is a really great forum and I am receiving tons of help. I like how people here are not just blurting the answers, but are actually feeding me ideas so that I may work them out...

Let,s suppose we wish to calculate the roots of a function f(x) f(x)=0 , of course you will say.."that,s very easy doc...just try Newton Method, fixed-point method or other iterative method"..the main "problem" we have is if f(x) includes non-differentiable functions such us the floor function...

Is there a good algorithm for computing such things modulo a prime? (I'll confess to not yet having tried to see if Shanks' algorithm can be easily adapted; I'll probably fiddle with that tomorrow)

If we define the function: F[w]=\int_{-\infty}^{\infty}dxe^{-iwx}g(x) my question is..what would be the criterion to decide if F[w] has all the roots real (w=w*) and how is derived?..thanks.

Considering the case of cubic polynomials with integer coefficients and three real but irrational roots. Is it true that it's impossible that all three roots can be in the form of simple surd expressions like r+s \sqrt{n} (where r and s are rational and sqrt(n) is a surd). The argument is that...

It,s proven that there can not be any Polynomial that gives all the primes..but could exist a function to its roots are precisely the primes 8or related to them) if we write: f(x)=\prod_{p}(1-xp^{-s})=\sum_{n=0}^{\infty}\frac{\mu(n)}{n^{s}}x^{n} wher for x=1 you get the classical...

Hello, I have two questions about this problem: (D^4 + 5D^2 + 4)y = 0 y(0) = 10 y'(0) = 10 y''(0) = 6 y'''(0) = 8 \lambda^4 - 5\lambda^2 + 4 = 0 (\lambda^2 + 4) (\lambda^2 + 1) Until here I am fairly sure that I didn't mess it up.. But I'm not sure if I have the roots...

this is a question that only mathematicians know about why the roots of the Polynomial: \sum_{n=0}^{k}a_{n}x^{n} with k>4 and integer can,t be obtained by elementary algebra (addition,substraction,and so on)..

Okay, before I start my discussion, note that k \in \mathbb{R} Edit: for anyone reading this right now, I accidentally hit 'submit post' instead of 'preview', so please ignore the thread until it has some content! Okay, here is the content. In my prof's notes, he is evaluating...

Please Help! I designed this "PROGRAM"! TO calculate the real roots of a quadratic equation... but the compiler miracle C kept saying there's something wrong around the "if" word... saying "unrecognised types in comparison" it seem SO FINE to me... what is wrong?!:eek: #include...

This is indirectly related to issues with cyclotomic polynomials and glaois groups. Is there some easy way to know if you are dealing with a cos or sin that is expressable in terms of roots of rationals? Like \pi/3 for example? If so, is there any straightforward way of figuring it out...

The first one, integration, I just want to check my answer. \int \frac{1}{64} (\cos6\theta + 6\cos4\theta + 15\cos2\theta + 20) = \frac{1}{64} (\frac{\sin6\theta}{6} + \frac{6\sin4\theta}{4} + \frac{15\sin2\theta}{2} + 20\theta + c I just wasn't sure if the integral of a constant wrt theta...

http://img522.imageshack.us/img522/7522/mat4vj.gif where X is the number into the term http://img524.imageshack.us/img524/2985/prob23ei.gif Computer F'(6) The square root is what's giving me my most difficulty. I don't know how to apply the term with a square root and computer f'(6)...