Roots Definition and 978 Threads

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. 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...

how do i take the derivative of sqr(4 + sqr(3x))? My teacher wants me to do it as a chain rule composition function so i separated it into F(x)= (4+x)^1/2 and G(x)= (3x)^1/2 but i don't know where to go from here because i don't know how to take the derivative of f(x)

Find the roots of the equation x^3 - 3x^2 - 10x +24 = 0 I personally, have never done cubic equations so can you please explain what should i do here. Should i try with GCF, even though i don't see one yet, or is there a method to do this?

Homework Statement Find the derivative from definition of the functin f(x)= x + squareroot(x) Homework Equations The Attempt at a Solution I only got as far as where I canceled out my positive and negative x terms in the numerator, and am left with three terms (2 of which are...

This is for 10th root unity with complex number multiplication. I am working on closure. I have multiplied 2 elements of my set and I have so far that cos[(n+k)360/10] + isin[(n+k)360/10]. Thus I know that if n+k<=9 then there is an element in the set. Now I need to show for if n+k>9 and if...

The question is as follows: \frac{lim}{h\rightarrow0} \frac{\sqrt{1+h}-1}{h} I don't know if the way I approached the question is right, I'll give you a step by step of what I attempted: First I converted the square root into 11/2 and h1/2 (can I do that? Is that correct?) Then I...

It seems that a significant other is a large potential for corruption. i.e helping you do or get things that someone else will not do due to being illegal. This is most clear when they have a job but break the rules of conduct to help you achieve something. Being friends with someone has a...

Hi, For a physics class, I am supposed to evaluate the following integral I_n(a) = \int_{-\infty}^\infty \mathrm dx \, e^{-n x^2/2 + n a x} \cosh^n(x) as a function of the real non-zero parameter a, in the limit as n \to \infty using the method of steepest descent. The question adds...

How do I solve: [sin (pi/3)] + [cos (pi/6)]? <--- "pi" is 3.14... I think that [sin (pi/3)]= (square root 3) divided by 2 AND that [cos (pi/6)]= (square root 3) divided by 2. Now I can't remember how to add fractions containing square roots. My textbook...

I came across an interesting article that discusses some recent research about the brain, its structure, and the relationship with aptitude. September, 2008 in SCIAM Mind & Brain Subheader - Researchers are finding clues to the basis of brilliance in the brain...

Homework Statement Find the range of values of k for which the roots of the equation are not real. Homework Equations y = x2 + (k - 2) x + (k + 3) The Attempt at a Solution I have no idea...

Homework Statement f(x)=24x7-13x6-19x5+7x4-7x3+5x2+72x-54 Find all the roots.. Homework Equations +-(p/q)...for rational roots The Attempt at a Solution i tried factor theorem,, and synthetic division for the possible roots..i've used uppe/lower bounds but i can't get a single...

Homework Statement Without using a calculator, find the solution to \sqrt[3]{0.64 * 10^8} The Attempt at a Solution Well, I figure I want to get everything into powers of 3. 4^3 = 64, but that leaves 100 as the denominator to get 0.64, which does not play well with ^3. I can split 10^8...

I've been working through "A Course of Pure Mathematics" and there is one problem I'm really stuck on. I'm wondering if anyone could help me out. To avoid typing it all out, I here's a link...

x^3-7x^2-10x-8 = 0 what are the roots?? Sorry, I am horrible at doing these kinds of things, this is for another problem in my differential equations thread. Its been so long since I did simple roots of a polynomial, I forgot how to do it LOL! and please, this homework is due tomorrow...

Hi, roots problem again x(. The roots of the equation x2 +px + 1 = 0 are a and b. If one of the roots of the equation x2 + qx + 1 = 0 is a3, prove that the other root is b3. [Done] Without solving any equation, show that q = p(p2 - 3). Obtain the quadratic equation with roots a9 and b9...

Show that the equation x2 + (3\alpha - 2)x + \alpha(\alpha - 1) = 0 has real roots for all values of α \in IR. How do i do this? Do i just use the b2 + 4ac \geq 0 ?

I find complex numbers very fascinating. But i don't understand something. Why does a cubic equation have 3 answers instead of 6? I know that there are 3 cube roots of a complex number, and the imaginary part of the complex number can be either positive or negative, so there should be 6...

find all roots of x^3 + 3x^2 - 10x + 6 the solution: identify the easy root of x=1, find the remaining roots from (x-1)(x^2+4x) using quadratic formula. The only thing i don't understand here is how to factorize to (x-1)(x^2+4x)... namely the (x^2+4x) part.

Homework Statement Determine how many roots the equation (z + \frac{i\sqrt{3}}{2})^{29} = \frac{1+i}{\sqrt{2}} has that are in the first quadrant. The Attempt at a Solution I would like to treat the right hand side in the following way. (z + \frac{i\sqrt{3}}{2})^{29} =...

If F is a field, how do we prove that a non-zero polynomial with coefficients in F and of degree n has at most n distinct roots in F?

[SOLVED] roots of a polynomial Homework Statement Let P(x) be a polynomial of odd degree with real coefficients. Show that the equation P(P(x))=0 has at least as many real roots as the equation P(x) = 0, counted without multiplicities.Homework Equations By the FTC, P(x) and P(P(x)) factor into...

Let r be a primitive root of a prime number p \geq 3. Prove that if p \equiv 1 (mod 4), then -r is also a primitive root of p. I've been told it's quite easy, but I can't see why it's true for the life of me :frown:

y = X^3 - 4x^2 -7x + 10 i have to draw a graph of this, stationary points don't matter but all else does. i know what it would look like because it is a cubic it will have 3 roots. but i don't know how to find them, i forgot :P can someone help please :)

Homework Statement Prove that if y1 and y2 have maxima or minima at the same point in I, then they cannot be a fundamental set of solutions on that interval. Homework Equations Do I take the wronskian (determinant of y1, y1', y2, y2')? What would that tell me? The Attempt at a Solution

how do i find the number of roots for a curve that has dy/dx 2x^4 -20x^2 + 50. if i substitute y=x^2 and use the discriminant formula i get b^2 - 4ac = 400 - 4 x 2 x 50 = 400 - 400 = 0 This way says there 1 root, answers say it has 2. Which method am i meant to...

Homework Statement simplify m^(9*√5)/m^(√5) The Attempt at a Solution would that equal m^9 or m^(8*√5)

1. Homework Statement [/b] ∫x/√(x-1)dx 2. Homework Equations [/b] I'm just stumped. I have tried u substituion with u=√(x-1) x=u^2+1 ((u^2+1)/u)du =(u+1/u)du but it doesn't seem to work and I can't integrate 1/u. I just don't know where to go with this any help would be...

hi there h r u >? i am a high school physics teacher, and i write many software in vb.net for simulation and ... the qustion i use Newton raphson method to find a root of function but i want to determine the following 1-is the function has a root or not, and then; 2-how can i find...

Pol degree 3, at most 3 real roots?? Well, i am trying to prove the following, indeed i think i have proved it, but it is just that it looks a little bit long, and i was wondering whether if first of all i have done it right, and second if there is any other method proving this using calculus...

Homework Statement Find the asymptotic formula for \sqrt{1}+\sqrt{2}+\sqrt{3}+\sqrt{3}+...+\sqrt{n} in the form of c \ast n^{\alpha} Identify c and alpha. (Do NOT use the fundamental theorem of calculus) Homework Equations Area under curve y = \sqrt{x} in [0, 1] is...

Sorry for the length of the post, the problem I've included is not difficult but I wanted to have an example to help illustrate my question. solve: \sqrt{x}-\sqrt[4]{x} -2=0 . . . (x-16)(x-1)=0 The roots are 16 and 1, however when one puts them back into the original equation, 1 is...

Homework Statement f(x,y)= ln(x+y) -x^2 - y^2 1. Find the partially derivatives 2. Find the stationary points (roots) of the function Homework Equations The Attempt at a Solution Quite simple, except i don't know what to do with the ln part, this is my attempt tho f'x=...

Starting with simple fractions, it's known that: {{{a \over b}} \over {{c \over d}}} = {{ad} \over {bc}} So when b == d: {{{a \over b}} \over {{c \over b}}} = {a \over c} But what if in the case of: {{{{1 + \sqrt 2 } \over {\sqrt 2 }}} \over {{{1 - \sqrt 2 } \over {\sqrt 2 }}}}...

1) Prove that the acute angle whose cosine is 1/10 cannot be trisected with straightedge and compass. ... I worked it out and at the end found out that , if I can prove that the cubic polynomial 40x3 - 30x -1 has no rational roots, then I am done. Now, is there any way to prove (e.g...

How do you get 3/sqrt2 from 3sqrt2/2?

Homework Statement y^6+1=0 Find the roots of this equation. (They are complex numbers) Homework Equations none. The Attempt at a Solution y^6+1=0 (zi)^6+1=0 z^6-1=0 [tex]y_1=z_1i=1i=i[/itex] How will I find other 5 roots?

If a is a perfect square then a is not a primitive root modulo p (p is an odd prime). (from Artin's conjecture on primitive roots) http://en.wikipedia.org/wiki/Artin%27s_conjecture_on_primitive_roots This is what I know: suppose a = b^2 a is a primitive root mod p when , a^(p-1) congruent to 1...