Roots Definition and 978 Threads

can roots be at the same points as POI's? because when I set my original equation to zero and I set my second derivative equation to zero i get the same answer? is it possible that roots can be same as the POI's.

Hello, I have a few questions! I need clarification on certain points that were not very clear in my calculus book. ---------- Question 1: I know that \int e^{ax} dx = \frac{1}{a} e^{ax} But how do you integrate \int e^{ax^2} dx ? ----------- Question 2: I know that...

Prove x^4 + 4x + c = 0 has at most two real roots My thinking is that to prove this I would assume that it has three real roots and look for a contradiction. So I set f(x) = x^4 + 4x + c and assume three real roots x_1, x_2, x_3 such that f(x_1) = f(x_2) = f(x_3) = 0 By MVT I...

I have two problems I'm working on that I can't figure out. Could anyone please help? 1. show that if p and q are distinct odd primes, then pq is a pseudoprime to the base 2 iff order of 2 modulo p divides (q-1) and order of 2 modulo q divides (p-1) I've been trying this proof by...

I was curious why primitive roots are so important? Also, how one would find out if a number has a primitive root and what and how many of them they are?

is there a method to compute roots other than sqrt?, like 10th root or 13th root of a number? and, what are they?

find the four roots of the equation z^4 + 7 -24i = 0 completely lost, some help please...

It is me again, 2 problems later I ran into another problem, I've submitted it a few different times but still is incorrect. Anyone see my mistake? I entered this as the answer: http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/a0/13092fac04d4a01ec22b57e193ed051.png Here is the...

i am to find the 4th roots of -16 (-16)^{1/4}=2i^{1/4} i=e^{i \pi/2} i^{1/4}=e^{i \pi/8} (-16)^{1/4}=2e^{i \pi/8} or (-16)^{1/4}=2e^{i 5\pi/8} or (-16)^{1/4}=2e^{i 9\pi/8} is this correct?

OKay i havn't gotten 1 2nd order Diff EQ right yet! I'm on a role! wee! Find y as a function of t if 81y'' + 126y' + 79y = 0, y(0) = 2, y'(0) = 9 . Here is my work: http://img204.imageshack.us/img204/4605/lastscan5ag.jpg I submitted this and it was wrong...

Hello everyone. I"m not getting this problem right. <insert sad face here> Find y as a function of t if 6y'' + 33y = 0, y(0) = 8, y'(0) = 5 . y(t) = hokay, here is my work, it is sloppy sorry. Can you see any obvious mistakes I made? Note: the sqraure root should be encompassing both the 11...

I am asked to use the exponential form e^{i \theta} to express the three cube roots of: (a) 1 (b) i (c) -i what exactly does this question mean? I am really lost as to what they are asking for. here is a stab at it: (a) cube root of 1 is 1... so... would that mean... 1=e^{- \infty...

i'm doing my online homework as we speak and they problem I'm on is this Use your calculator to find the square root of 6.70 × 10^-19 and i calculated that problem in my calculated and i got 6.7e^-19 and i typed it in my homework and its giving me an error and saying "This question...

Hello All I am trying to figure out how to determine if there are two, one, zero, or infinitely many roots for given formula ax^2 + bx + c. Are there any easy ways to determine this without having to use the quadratic formula? Thanks P

Question that I came across and that has stumped me for about a week hehe. Let p(z)=z^n +i z^{n-1} - 10 if \omega_j are the roots for j=1,2,...,ncompute: \sum_{j=1}^n \omega_j} and \prod_{j=1}^n \omega_j}

for sqr root of (n + sqr root (n) ) - sqr root (n),is the answer = zero or infinity so converges or diverges??

find all solutions of the given equation: (z+1)^4=1-i im not sure if i did this right, but here's what i did the first thing that i did was notice that 1-i = 2^1/2 * (cos (pi/4) + i*sin(pi/4)) then i found z= [2^(1/2*1/4) * (cos (pi/4) + i*sin (pi/4) )^1/4] -1 then using de moivre's thrm...

Does anyone have insights or a perspective on the possible biological roots of PA behavior (or disorder)? I am not a psychologist, psychiatrist, or biologist, but when I think of the evolution of the species it kind of seems obvious that the mammals lived a hard life under the dinosaurs' feet...

Since one can construct the length of a non-integer square root by drawing accurate triangles, and can draw a circle with a circumference of pi, then shouldn't one be able to plot corresponding non-integer square roots and pi on a number line? I know these numbers are supposedly irrational, but...

I have the definition that if F is a finite field then a \in F is a primitive root if ord(a) = |F|-1. Now what I don't understand is how exactly are there \phi(|F|-1) primitive roots? (Note: This material is supposed not to use any group theory.)

If ar^2+br+c=0 has equal roots r1, show that L[e^(rt)]=a(e^(rt))``+b(e^(rt))`+ ce^(rt)=a{(r-r1)^2}e^(rt) could someone offer some advice?

All the roots of a real function f(x) are real unless. 1.K(x) is a Polynomial of degree k 2.f(x)=exp(g(x)) where g(x) is different from ln of something 3.f(z) with z=u+iv is invariant under the transformation of v=-v with f(u+iv)=F(u-iv).. 4.the function f includes some of the functions...

Let be the Quantum Potential V(x)=A(x)+iB(x) with A and B real functions then my question is if this potential will have real roots if we take the expected value: E_{n}=<\phi|H|\phi> then the complex part of the energies will come from the expected value <B> so for real energies B should be...

I'm not sure whether this is the correct forum, so I apologise if it's in the incorrect forum. Anyway, when studying A level maths a few years ago, we came across a technique for calculating roots that my teacher claimed was used before calculators were invented. I can't remember the actual...

why is it that when you have the same roots to an O.D.E., you usually add an x or x^2 to get a basis?

Hey having a bit of trouble with this question, not sure what to do! QUESTION - express the fraction in the form a + b rootc / d 3 + root24 / 2 + root6 ------------------------------------------ (3 + root24 / 2 + root 6) x (2 - root 6 / 2 - root 6) Simplifying gives (6 -...

Ok, i got two funktions: b1:=(x/10)+sin((x/3)+(Pi/2)); and b2:=(1-2*cos((x/4)+(Pi/2))); I need to determine all the roots between 0 < x > 30 If I plot the functions i see that there should be two roots plot([b1,b2],x=0..30); But when try to get maple to calculate the roots It only...

hello how can i finding roots to cubics?? explain by example :smile:

let be the function f(x) so we have that if x is a root also x* is a root, but we have that x is NEVER a pure imaginari number,i mean x is always different from x=ia the my question is if this means that all the roots will be real,the only counterexample i find is...

x^2 +6x +k=0 has one root (a) where I am (a) =2, If k is real find both roots of the equation and k So i got b+ 2i is the root (b+2i)^2 +6(x+2i) +k=0 and after expanding it out, i have no clue what to do. Please help. THanks

How would I go about finding a number that is a primitive root modulo 125? There definitely exists a primitive root since 5^3 =125 The problem basically comes down to finding 'a' (primitive root); a^50 congruent to -1 (mod 125) Anyone know a way apart from trial and error? Thanks

I am in a Systems and Vibrations class but am currently doing differential equations. A problem I am doing requires me to find the transfer function [X(s)/F(s)] and compute the characteristic roots. So far I have: X(s)/F(s) = (6s +4)/(s^2+14s+58) That is the transfer function but now...

If m, n, and 1 are non-zero roots of the equation x^3 - mx^2 + nx - 1 = 0, then find the sum of the roots This is what I did.. m, n, 1 are the roots. m and n not equal to 0 x^3 - mx^2 + nx - 1 = 0 f(m) = 0 --> m^3 - m^3 + mn - 1 1 = mn (1) f(1) = 1 - m + n - 1 = 0 ... m = n (2)...

In seeing various related topics in PF regarding the reasons for terrorism, solutions for terrorism, the effects of the Bush administration on our country and the world, and more recently nuclear proliferation via the Bush Doctrine, I thought I’d start this new thread, which also may provide...

Can a number have more than 1 primitive root? Thanks

Hi, I came across this puzzle, see if you can solve it :smile: : \sqrt{1 + \sqrt{1 + 2\sqrt{1 + 3\sqrt{...}}}} = ?

let be the quotient: Lim_{x->c}\frac{\zeta(1-x)}{\zeta(x)} where x=c is a root of riemann function... then my question is if that limit is equal to exp(ik) with k any real constant...thanks... the limit is wehn x tends to c bieng c a root of riemann constant

Hi all Jut had a question. How do I go about finding the general formula for roots of the complex poly {z}^{n}-a where a is another complex number. Do I just go {z}^{n}=a? :S so complicated this things! Thanks in advance!

Let be the function h(x)=f(x)+g(x) we want to obtain the values of x so h(x)=0 and we have that f(x) and g(x) have the same roots (if a is so f(a)=0 then g(a)=0 too) so we have two types of roots: 1.-values of x that satisfy f(x)=-g(x) 2.values x that make f(x)=g(x)=0 then we make in the...

There are n nth roots to every complex number (except zero). My question: How many "roots" are there when you take a complex number to an irrational or transcendental number. For that matter, how do we define raising a number to an irrational number? How do we define raising a number to a...

Q. Fix n>= 1. If the nth roots of 1 are w_0,...,w_(n-1), show that they satisfy: \left( {z - \omega _0 } \right)\left( {z - \omega _1 } \right)...\left( {z - \omega _{n - 1} } \right) = z^n - 1 I tried considering z^n = 1. z^n = e^{i2\pi + 2k\pi i} \Rightarrow z =...

This may be a bit silly but i forget how to factor this into complex factors: s^2 + 6s + 25 i know the answer is (s +3 - i4)(s +3 - j4) but how do i get that?

I was curious about what class would cover those types of Linear DE w Constant Coeff, particularly Hyperbolic Functions and exp z type of things. I remember my lecturer said back in Intro DE that we only covered first 2 types of Auxiliary Equations - real distinct roots and real repeated ones...

Problem: If c_{1}, ..., c_{n} are the complex roots of a_{n}z^n + a_{n-1}z^{n-1} + ... + a_{1}z + a_{0} = 0 with a_{n} not 0 and S_{k} is the sum of the products of these roots taken k by k, then S_{k} = (-1)^k . \frac{a_{n-k}}{a_{n}}. Prove this by using induction. So for n = 3 this...

Hi, How is the roots of a quadratic equation related to the distance from the x-axis at where the root is - where ... ax^2+bx+c=0 and ... x = (-b +- SQRT(b^2-4ac))/2 Can someone help me to establish where this distance relationship to the x-axis and the root come from? Thx! LMA

Hi, A cubic equation has at least one real root. If it has more than one why are there always an odd number of real roots? Why not an even number of real roots? Can someone help me to prove this? Thx! LMA

I've been trying to derive general solutions for cubic roots, i.e. the general solutions of (will Latex just work?) $ax^3+bx^2+cx+d=0$ I do not want to be shown the solutions - but does anyone know what direction to go into achieve this? I thought I'd found solutions at one point but...

Hi guys, can anyone tell me how I would go about solving this equation? : x^5 = x Rearranging it gives: x^5 - x = 0 But then I don't really know what to do next. I know just from looking at it and thinking about it that the roots should be x = 0, 1, -1, -i, i...but I need to be able to...

What are some good quick ways to Extract Square Roots in your head. I'm looking for a method that is very prescice and easy thanks, hopefully somebody helps me out

hello. I was wanting to know how to raise a number to any power without using a calculator. More specifically, I was wanting to raise numbers to the .5 power, (and all the other roots, 1/2, 1/3, 1/4). How can this be done? <----------------------> My fellow 633|<5 :smile: