# Tagged Questions

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### How to find all complex polynomial $f$ such that $1+f(z^n+1)=(f(z))^n$

Question: Let $n\gt1$ be a natural number. Is there a non-constant complex polynomial $P$ such that $P(x^n+1)=P(x)^n-1$ for all $x$? I saw this problem about polynomial, here is the question: Find ...
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### Factor the equation either by pairs method or any other [closed]

I tried to split by pairs but i got nowhere. $$x^2 - 4y^2 - 4x + 4$$
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### Understanding Multiplicities

I am having troubles understanding what 'multiplicities' mean. In example what does $-1/3(multiplicity 2)$ translate into?? To clarify this is for finding zero's in a polynomial function Any help ...
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### Prove, that two equations are equivalent

EDIT: Missed something very important! Sorry! We have $x^4+1=2(2x-1)^{1/4}$ not $x^4+1=2\sqrt{2x-1}$. One friend of mine told me that the equation $x^4+1=2(2x-1)^{1/4}$, where $x\geq \frac{1}{2}$ is ...
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### Solution of a partial fraction equation

Consider the equation in the variable $\lambda$ \begin{align} \sum_{i=1}^{N}\frac{a_i}{(\lambda+b_i)^2}=1 \end{align} where $a_i$ and $b_i$ are all positive. How do you find any solution to this ...
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### Find $g(x)$ if $f(g(x))=f(x)g(x)$ and $g(2)$=37, $f(x)$ and $g(x)$ are polynomials

Suppose $f(x)$ and $g(x)$ are non-zero polynomials with real coefficients, such that $f(g(x))=f(x)\times g(x)$. If $g(2)=37$, find $g(x)$. I tried plugging $f(x)$ and $g(x)$ as $n$ and $m$ ...
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### Get polynomial function from 3 points

I need to understand how to define a polynomial function from 3 given points. Everything I found on the web so far is either too complicated or the reversed way around. (how to get points with a given ...
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### given the polynomial function find the function values

I given a problem and I can not get to the answer that I was given by my professor. P(x) = -x^2 - x + 12 where P(-2). I keep coming up with 10. He gave me the answer of -2. Am I missing something?
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### Finding roots of a function in an interval

Does the equation $x^3-12x+2=0$ have three solutions in the interval $[-4,4]$? We know that this is a continuous function because it's a polynomial, and so we can use the Intermediate Value ...
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### Conversion of roots of a polynomial

I'm wondering, given a polynomial $P(x)$ with roots $r_i (1\le i\le n)$, how to determine the polynomial $Q(x)$ such that its roots are $r'_i=f(r_i)$. For example, if $P(x)=x^2-x-6=(x-3)(x+2)$ and ...
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### A physics related question about an infinitely long pipe.

This is a really nice question I found some days ago, so I translated it into English to share. Suppose we have a water pipe which is infinitely long, with water flowing in it. We know that if a ...
I have a problem that asks me to find a polynomial $P(x)$ so that $P(3)$ is 9. Now I can say with certainty that $P(x)$ can be $x^2$. This is a second degree polynomial. But what about functions ...
### Find the equation with roots, $A$, $B$, $C$ is $ABC=6$, $A+B+C=5$ and $A^2 +B^2+C^2=21$
Find the equation with roots, $A$, $B$, $C$ is $ABC=6$, $A+B+C=5$ and $A^2 +B^2+C^2=21$ Can someone please hint me, or show me what do i do with this question please. Im quite clueless and need to be ...