In vascular plants, the roots are the organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They most often lie below the surface of the soil, but roots can also be aerial or aerating, that is, growing up above the ground or especially above water.
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.
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
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...
Situation: I had tired a 1000-data generated by random error(i.i.d.), then I sub it into different unit root tests. I got different results among the tests. The following are the test statistics I got:
For R project:
adf.test @ tseries ~ -10.2214 (lag = 9)
ur.df @ urca ~ -21.8978
ur.sp @...
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 +aix+bi
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 possible) be in one...
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?
I'm working on the limit of the sequence
(Xn) = (n!)^(1/n)
Pretty sure it diverges as n goes to infinity,
but unsure how to show it.
Any hint would ge greatly appreciated.
Homework Statement
This problem is #17 in Chapter 3 of Giancoli's 5th Edition Physics.
The summit of a mountain, 2085 m above base camp, is measured on a map to be 4580 m horizontally from the camp in a direction 32.4 degrees west of north, What are the x, y, and z components of the...
Integration of a composite square root function, easy (hard for me :( )
Homework Statement
How would I integrate:
y = \sqrt{(1 + 4x^2)}
Homework Equations
-
The Attempt at a Solution
I have no idea how to do this. I tried to to the chain rule in reverse, and then I ignored it, but I can't...
Homework Statement
find \int x^{\frac{3}{2}}\sqrt{1+x} dx
Homework Equations
The Attempt at a Solution
Now i tried all the methods i know of which include integration by parts and substitution,the integration by parts didn't work too well, so substitution I tried.
let...
Am sorry, if this topic does not belong to this section, as i am new, kindly oblige
Can root RMS value of current (what we study in Alternating currents) be negative?
i feel that it can surely be negative as it is a root, but my teacher told that it can't be negative and showed just one...
This is just a general question:
If, when you are calculating the eigenvalues for a matrix, you get a root of 0 (eg. x^3 - x) --> x(x-1)(x+1), what does that mean for the eigenvectors?
thanks,
w.
Homework Statement
Find a Polynomial function of degree 5 whose zeros are: 2, radical 7, and 5i Homework Equations
Multiplying rootsThe Attempt at a Solution
Hello, well it's my first time at these forums so just following the template given. Thanks for any help by the way I'm just so...
I'm confused on the graph: y=\sqrt{x}-4
I know the x- and y-intercepts which are: (0,-4) and (16,0) but I don't know if the graph extends to the negative x (3rd Quad). You can never square root a negative number and get a real number right? Therefore, does the graph just stop at the...
thoughtful paper on how to convey an idea with least confusion
http://arxiv.org/abs/0707.0380
Expanding Space: the Root of all Evil?
Matthew J. Francis, Luke A. Barnes, J. Berian James, Geraint F. Lewis
8 pages, accepted for publication in PASA
(Submitted on 3 Jul 2007)
"While it remains...
Is "root over a^2=modolus of a?"
mod of a is always positive, but root over a^2 can both be positive or negative. So how these two can be equal to each other?
I have found this in a math textbook. But I can't convince myself about it.
It will be very helpful if you give a proof.
Thnx in...
Isn't \sqrt{2}^{4} equal to 4?? How come when I plug this into my calculator it gives me the number:3.999999999996 , which is very close to 4 but isn't?? Is there something wrong with the settings of my calculator?
Root of "n" degree of the number "n"
Hello!
Frankly speaking I am not sure whether this is proper forum, because I am not sure if this exercise involves calculus or not...
The task is:
Consider the numbers "root of "n" of n degree", n >= 2. How many of them are equal? Justify your answer...
Mosses and ferns have rhizome whereas a mango tree has root.
Rhizomes are used for absorbing water and nutrient from ground by mosses as higher plants use their roots. SO I don't understand why two distinct terms are used for things of similliar functions.
I am having a hard time figuring this out.
Suppose we have a 4x4 matrix A, B and rotation matrix D.
Matrix A represent position and orinetation of object1, matrix B represent position and orientation of object2. Matrix D is the position and oreintation of object2 relative to object1.
B = D*A...
I've been looking at the value N(n) of N that satisfies the equation
\sum_{1}^{n}(N-i)^{n}=N^{n}
Thus turns out to be
N(n)=1.5+\frac{n}{ln2}+O(1/n)
where the O(1/n) term is about 1/400n for n>10.
I've verified this by calculation up to about n=1000, using Lenstra's long...
I feel embarassed to ask these questions but what is the rule for to simplify division, addition, and subtraction square roots? Here are some questions:
SIMPLIFY:5\sqrt{24}\div2\sqrt{18}
\sqrt{40} + \sqrt{90}
\sqrt{50} - \sqrt{18}
As a Grade 12 student that is often required to find the roots of quadratics for math, physics, and chemistry problems, I wondered whether there would be any methods for solving these problems excepting the quadratic formula. I was pondering the implications of calculus in algebra and, although...
Homework Statement
derivate: x^2 \sqrt{x}
Homework Equations
(u \cdot v)^\prime = u^\prime \cdot v + v^\prime \cdot u
The Attempt at a Solution
I found:
(x^2)^\prime = 2x
(\sqrt{x})^\prime = \frac{1}{2 \sqrt{x}}
I entered them into the equation:
2x \cdot \sqrt{x} + x^2...
Homework Statement
Does this series converge or diverge?
Series from n=1 to infinity n(-3)^(n+1) / 4^(n-1)
Homework Equations
The Attempt at a Solution
Okay, I've tried it both ways.
Ratio test:
lim n --> inf. ((n+1)*(-3)^(n+1)/4^n) / (n * (-3)^n / 4^(n-1))
Now...