Roots Definition and 962 Threads

I'm reading a chapter on recurrence relations and they have a problem with the phrase: ...if r is a root with multiplicity 2. What does it mean for a root to have multiplicity? This is the first time I've heard of this and the book assumes I would know what they mean already.

hello everyone, this is my first post.. I've got myself a problem. say I have a field F, and that f(x) is a polynomial with coefficients in F. (all the normal differentiation rules apply like always.. product rule, quotient rule, etc.) Now, I know that a polynomial f(x) has a "multiple...

Such as sqrt 5: (2.236067977...) Start with the fractional seeds 2/1, 9/4,... New members are generated (both numerators and denominators) by the rule new member = 4 times the current plus the previous. Which generates the progrssion 2/1, 9/4, 38/17, 161/72, 682/305, 2889/1292...

Hello, I have a simple equation (maybe simple for some) that I can't understand how to get from one point to the next when re-arranging. If you can help by giving an answer in english I would be thankful... The equation T = 2 pi square root L / g (sorry couldn't find the square root...

u noe how x^5=1 has 5 roots which some of them are not real in complex field. and so is x^2=-64 with roots = -8i or 8i and i notice that the sum of roots = 0 (msut inculde non real --> complex number) is this becasue of the rule of polynomial --> -b/a =...

How can i find the derivative of a function like this: f(x) = sqrt( 1 - x² )

Hey I’d really appreciate some help with these problems (they should be fairly easy, I just can’t seem to remember how to do them): (1) Find the range of k, element of R, for which x^2 + kx + k = 0 has real roots. If one of the roots of this equation is 2, find the other root. (I’ve proved...

Hi...I know what Sine, Cosine, and Tangent represent in math and how they are used...but I'm asking a different question. That question is: how are they calculated? That is, when I put, say Sine(10) into a calculator, how does it calculate that value? Additionally, how are square roots...

I have a question. You might be familiar with the following expression for the golden ratio: X = \sqrt{1 + {\sqrt{1 + {\sqrt{1 + {\sqrt{1 + {\sqrt{1 + ...}}}}}}}}} For those who haven't seen this before, to solve this we just square both sides (which removes the outermost square root...

I'm trying to find the: 4 4th roots of [itex] {\sqrt{3}} [/tex] + i . So I made a Cartesian plane and graphed radical 3 and 1.. but these numbers can be in 2 quadrants, 1st and 3rd. r=2 ==> 2([itex] {\sqrt{3}} [/tex] + i) ===> 2(cos 30+isin 30)...

on a ti83 calculator, how do you put in cubic roots?

What's the most easiest, simplest way of figuring out square roots?