Roots Definition and 962 Threads

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...

[SIZE="3"][SIZE="4"]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...

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...

Homework Statement Barry has just solved a quadratic equation. He sees that the roots are rational, real, and unequal. This means the discriminant is a) zero, b) negative, c) a perfect square, d) a non perfect square Homework Equations The Attempt at a Solution I think the...

Hi, I am getting frustrated with trying to solve this equation: sqrt(x+9) - sqrt(x-6) = 3. I know that the answer is x=7 because of guess and check. I don't know how to show it algebraically. Squaring both sides will cancel out the x. Is there a trick or something this? Please help...

Hello guys can anyone help me solve this in MATLAB please ? http://aycu34.webshots.com/image/43953/2003131790943491216_rs.jpg

if o,p,q are roots of the equation ax^3+bx^2+cx+d=0, determine the equation whose roots are o^2,p^2 and q^2 who can help me solve it? thank you

Ok. I have a definite integral of e^sqroot(x) dx from x=0 to x=1. I would use u=sqroot(x) and du=1/2*sqroot(x), but I'm confused what I would set v=?

zero's and roots... Zero's are the same thing as roots, correct? I have a question where a) askes what's the zero's. Then b) asks what are the roots. pretty sure it's the same.

Homework Statement Hi guys, i have never taken number theory yet now I am forced to quickly understand it as it was required for a class i signed up. I need help with these problems and would greatly appreciate any hints or help in the right direction. Thanks. 1)Find with proof, all n such...

I'm having trouble understanding the idea of a weight space. Suppose \mathfrak{g} is the Lie alebra of G with maximal torus T and Cartan subalgebra \mathfrak{t}. The weights are the (1-dimensional) irreducible represenations of T. If we restrict any representation \rho : G \to GL(V) to T...

Homework Statement Find the roots of the equation z^3=-(4\sqrt{3})+4i giving your answers in the form re^{i\theta}, where r>0 and 0\leq \theta<2\pi Denoting these roots by z_1,z_2,z_3, show that, for every positive integer k. z_1^{3k}+z_2^{3k}+z_3^{3k}=3(2^{3k}e^{\frac{5}{6}k\pi i})...

Homework Statement Given Lim Cn=c, Prove that Lim\sqrt{Cn}=\sqrt{c} Homework Equations We are working from the formal definition: for all \epsilon, there exists an index N such that For all n>=N, |Cn-c|<\epsilon The Attempt at a Solution We as a group have attempted this several...

Homework Statement The roots of the equation x^3-x-1=0 are \alpha,\beta,\gamma S_n=\alpha^n +\beta^n +\gamma^n (i)Use the relation y=x^2 to show that \alpha^2,\beta^2,\gamma^2 are roots of the equation y^3-2y^2+y-1=0 (ii)Hence, or otherwise find the value of S_4 (iii)Find...

A few of the (assumed to be good) textbooks on College Algebra discuss the use of Descartes Rule of Signs, and a test for upper and lower bounds for real zeros for polynomial functions; but these ideas are never proved in the books that I found. In which college course, and in which Mathematics...

Homework Statement \frac{5}{\sqrt{7+3\sqrt{x}}} = \sqrt{7 -3\sqrt{x}} Homework Equations none The Attempt at a Solution does this equal 5 = 7 - 3\sqrt{x}