Root Definition and 918 Threads

Homework Statement show that the equation 1 + 2x + x^3 + 4x^5 = 0 has exactly one real root Homework Equations The Attempt at a Solution i don't know what to use to find out that it has exactly one real root. i know you use the intermediate value theorem for roots but what do...

Hi, I just registered on to the forums, and I have to say it is a very good job. I am currently a senior at High School and aiming for an Engineering Course. While solving some integrals, I got stuck upon this one, and even after a lot of attempt, my friends and I could not solve it. Hence I...

I am on my final part of my C3 coursework, doing the comparison of methods, i have found the root using the change of sign method, and the Newton raphson method but i am struggling with using the rearranging method. the equation i am using is x^3 +5x -4, i have tried rearranging it to get the...

Homework Statement Calculate \int_{0}^{4}\sqrt{x} e^{\sqrt{x}) The Attempt at a Solution At first I tried substitution, but this didn't bring me anywhere since the integral is not of the form \int f(g(x))g'(x) My attempt at integration by parts also leads to an endless loop...

Hi everybody... http://www3.0zz0.com/2008/07/02/08/264668819.jpg As shown in the previose figure, the output from the op amp is sequre root the input signal. Since the feedback of our circuit is sequare the feedback signal ( the output), we shall expect the output to be sequare root for...

Homework Statement Use the differential dy or L to approximate cubed root 1.03 Homework Equations L(x)= f(a) +f'(a)(x-a) The Attempt at a Solution I have no clue how to start so that would be the most help, do i just find the derivative of cubed root 1.03 first?

Hi. I'd like to show that sqrt(x*(x-1)) has the asymptote x-0.5. The coefficient on "x" is found by saying \lim_{x\rightarrow\infty}\frac{\sqrt{x(x-1)}}{x}=1 but how does one find the 0.5 constant?

Consider the function y=x^3 - 2x^2 + k, where k is a constant. Explain why k=0 ensures that f(x)=0 has a double root. A double root is a bounce and I thought that when k=0, the x^2 can be immediately common factored out of the function, so you have (x^2)(x-2)=0. Therefore, you will always have a...

I'm pretty sure it's not possible but if anybody has any kind of theory on finding the square root of a negative number go ahead share. Sorry if I sound a bit imature or "noobish". I'm new here and probably younger then a majority of the users here. Example: -100

Actually, can you take a root of any negative number?

1st I assume it is rational so: 7^(1/7) = m/n then 7 = (m^7)/(n^7) implies m^7 is a multiple of 7. Means m^7 = 0 mod 7 So, using fermats little theorem.. m^7 = m mod 7 for m to be in the class of 0 it has to be a multiple of 7. Now set m = 7k, so 7n^7 = 49k^7 But...

Homework Statement The reaction 2Fe3+ + Ni(s) = 2Fe2+ + Ni2+ has equilibrium constant K = 1.5E34. What is the concentration of Fe3+ at equilibrium if a lot of Ni(s) is added to a 0.1 M solution of Fe3+ that initially contains no Fe2+? The Attempt at a Solution K = 4x3/(0.1-2x)2 My...

If have a system with 4 open loop poles, all at say s=-2, how would the locus approach each of the four asymptotes? thanks

Homework Statement I have been doing elementary algebra for a couple of weeks now, and gotten quite used to the idea that the square root of n gives +- n1. Then moving on to arithmetic and n-roots / powers, I was given the current definition of the square root: The square root of a...

I am thinking that if the imaginary number is bigger than the other number, is it right to say that: i> 5 ? 7i> 3i ? Does i has magnitude? if Z_1=4+5i then Z_2=1-3i whether Z_1>Z_2 or Z_2>Z_1 is true? If we say Z_a is bigger than Z_b, does that means the absolute value of these complex...

[SOLVED] Re: Integral involving square root of e^x Homework Statement \int \sqrt{1-e^{-x}} Homework Equations Sub rule. The Attempt at a Solution I realized that it's fairly obvious I can use u=e^-x/2 to give \sqrt {1-u^2} but I'm kind of looking at the answers and I'm not seeing how I...

If one 4\times 4 matrix have two vanishing eigenvalues, does the matrix have a square root?

Ok, so doing a physics problem the other day I had to find a point c on a graph such that there was an equal amount of area between 0 and c and c and a point b > c. I found that for the graph f(x) = kx, the point was b over the square root of 2. This intrigued me so I looked for a...

Where on the imaginary number axis do i graph sqrt(3i)? At sqrt3?

1. find the antiderivative of sqrt(81-x^2) in the bounds 0 to 9/2 okay so the first thing i did was sin substitution. where I made x = 9sin(t) dx = 9cos(t) where t is theta. then after some manipulating i got that that new integral was 9cos^2(t) i then used the double angle formula and...

Homework Statement Solve this equation, and find x. 6x^5-5x^4-29x^2-5x+6=0 Homework Equations if x= \alpha is root of the symmetric equation, then x= \frac{1}{\alpha}, is also root of the symmetric equation The Attempt at a Solution I tried first to write like this...

Have this question in relation to some investment exam I am doing, I am a maths novice being some years since leaving school etc, ok enough of the excuses. Example FV = future value PV = present value R = interest rate N = number of compounding periods my PV is 6000 and my FV is...

Homework Statement Show that the square root of 3 is not rational Homework Equations The Attempt at a Solution A number is irrational if χ is not ε. Q=p/q: p, q ε z and q is not=0, z=integers If p/q: p, q is not ε or q=0, then square 3 is rational. If p=square root of 3 and q...

Homework Statement If the translationa speed of the water vapor molecules (H2O) in ir is 648 m/s, what is the translational rms speed of the carbon dioxide molecules in the same air? Both gases are at the same tmperature. Homework Equations V^2 = (3kT)/m The Attempt at a Solution...

According to Wikipedia, if n is odd, then every real number A has a unique real nth root having the same sign as A and known as the principal nth root of A. It is denoted by \sqrt[n]{A} My question is, how do we know that this is true i.e. that \sqrt[n]{A} exists for all real numbers...

Hi , is there a method to obtain the roots of Polynomials: P(x)=a_{0}+a_{1}x+a{2}x^{2}+...+a_{n}x^{n} i know there are , but my problem is this if we knew that are complex roots of the form z=a+ib , would be a method to obtain the complex root with BIGGER and SMALLER real part ?? , i mean...

[SOLVED] latex question How do you get a cube, fourth, fifth root in latex? I mean how do you get a little 3 to appear in the upper left next to the square root sign?

Homework Statement I want to know what's the formula to calculate the sum of the square root of integers from 1 to n. I got an identity from wikipedia but its too complicated for me, it involves bernoulli's number, i don't know what is that. Homework Equations The Attempt at a...

Homework Statement Prove that the diagonals of a parallelogram bisect each other. Homework Equations I chose one vertex as the origin, one as a and one as b. The final vertex was a+b. The Attempt at a Solution The diagonals were \vec{r_1}=\vec{a}+\vec{b} and \vec{r_2}=\vec{b}-\vec{a}...

Homework Statement An equation in a book lists this equation: (c - 18)^{2} = (-3\sqrt{c})^{2} And it simplifies it as: c^{2} -45c + 324 = 02. The attempt at a solution When I do out the equation, I get: c^{2} + 324 = 9 + c i squared c, then -18 for the left side of the equation, then for the...

Homework Statement a) Show that for small values of x, xtanx is approximately equal to x^2 and 2 - coshx is approximately equal to 1 - 0.5(x^2). Draw a conclusion from this regarding the probable number and approximate locations of roots on the interval [-1,1]. b) Use Newton's method to...

I was just going through some problems in a maths journal for undergraduate level i found a sum seeming simple but i am not able to solve it completely find domain of \sqrt{x^{12} - x^9 + x^4 -x +1}i know domain includes all negative value , all positive value >1 , but i can't get anything...

reducing sqrt(4t^2+4+1/t^2) to (1+2t^2)/t The Attempt at a Solution - This is actually just a portion of a calculus problem, but I can't figure out how the book did the algebra here. I get (2t^2+2t+1)/t and don't know how that reduces to (1+2t^2)/t. Please help.

how do i integrate: square root of((x^2)-4) i know i have to use substitution but what do i substitute?

Hello! I am just working through Zee's Quantum field theory in a nutshell and have a little problem. He calculates the free propagator and evaluates an integral (I doubt the integral is important for my question) when he writes "and the square root cut starting at \pm i*m leads to an...

Integral with sq. root in it...again Homework Statement Find.. \int x^\frac{3}{2}\sqrt{1+x} dxHomework Equations The Attempt at a Solution Well I used the fact that: \sqrt{1+x}=\sum_{n=0} ^\infty \frac{(-1)^n(2n!)x^n}{(1-2n)(n!)^24^n} and well I just multiplied by x^\frac{3}{2} so I...

Is there any "pencil and paper" method to find the nth root of a number? Since multiplying a number by itself any number of times quickly yeilds extremely large numbers, trial and error might seem to pinpoint the root of a number, so long as it is a perfect square or cube or whatever. But...

Homework Statement Determine whether the series converges or diverges. \sum_{n=2}^{\infty}\frac{1}{(\ln n)^{\ln (\ln n)}}=\sum_{n=2}^{\infty}\frac{1}{e^{\ln (\ln n)\ln (\ln n)}} The Attempt at a Solution for u=\ln (\ln n) \sum_{u=\ln (\ln 3)}^{\infty}\frac{1}{e^{u^2}}...

Homework Statement Integral from 1 to infinity of 1 / xln(third root of x) 2. Homework Equations n/a 3. The Attempt at a Solution I tried to find if it diverged and then got lost after that Homework Equations The Attempt at a Solution

What's the difference between a zero and a root? cheers.

Hi, I've encountered this exercise which I'm having a hard time proving. It goes like this: Prove that if m and n are natural, then the nth root of m is either integer or irrational. Any help would be greatly appreciated. Thanks.

I still remember how to extract a square root without a computer but could somebody remind me the technique to find a cubic root just with the pencil and paper?

Homework Statement State the number of complex roots and then identify what the roots are. Equation: 18x^2 + 3x -1 = 0 Homework Equations The Attempt at a Solution There are 2 complex roots. Okay. So I can't factor anything out of the equation and when you try to factor it...

Homework Statement For the double integrator described with transfer function G(s) = \frac{1}{s^2} the initial condition is zero. The double integrator is subjected to a unit‐feedback system where the controller is chosen as 1) a PI-controller with C(s) = k_p \left( 1 + \frac{1}{s}...

Homework Statement Number Theory homework. I'm supposed to prove that the value 2^.5 + 3^.5 is irrational by finding a monic polynomial that the aforementioned number is a root of. This would be trivial if I were supposed to prove that just 2^.5 was irrational because its monic polynomial...

Homework Statement The problem is really about finding the length of a parametrically defined curve, this in itself seems easy enough, but it's the integration part that's hard. The problem is as follows: x = cost y = t + sint t = 0...pi The Attempt at a Solution So in order to...

1. Homework Statement : We have 'n' quadratics is the form x^2 +a[SIZE="1"]ix+b[SIZE="1"]i All values of A and b are different. Is it possible to have all values of A and B as the roots of the n quadratics 2. The attempt at a solution: Well. I know that all values of 'a' and 'b' must (if...

FIRST What is the HIGHEST root? If there is a highest root, are there available any LOWEST root? Say, what is the highest and lowest root of f(x) = x^2 - 2x + 1? SECOND What happen if I sum the EVEN and ODD function? I don’t think I am a good on geometry. THIRD What is the integral of...

Hi guys, How would you prove that \sqrt[3]{7} is irrational without using the unique factorization thrm? I tried proving that \sqrt[3]{7} is rational but it didn't seem to get me anywhere... Thanks EDIT: Looks like I posted this in the wrong forum.

G'' = -kG k is a constant solving this ODE, r = +/- sqrt(-k) if k > 0, then r = +/- sqrt(k)i so G is in the form Acos(sqrt(k)x) + Bsin(sqrt(k)x) so, what if k is a complex number, then r = +/- sqrt(-ki) then what is the form of G?