# Tagged Questions

This tag is used for both basic and advanced questions on polynomials in any number of variables. Including, but not limited to: solving for roots, factoring, checking for irreducibility. This tag is rarely used as the only tag for a question.

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### Complex solutions within unit circle

How many solutions within a unit circle $|z| < 1$ does the equation $(1 + z)^{n + m} = z^n$ have for $z$ complex, and $n$, $m$ positive integers?
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### Finding an interval in which all the real roots of a polynomial lie

I'm making a program which uses simple bisection method to find the roots of a polynomial. For me to implement this method, I need a rough interval where it can be said with absolute certainty that ...
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### fifth degree equation

The general form of the fifth degree equation to achieve Bring-jerrard form some coefficients are complex . Should they be considered only real part of the coefficients that the roots of the fifth ...
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### Polynomial that is irreducible over $\mathbb{Q}$ but reducible over every finite field [duplicate]

I want to prove that $X^4 - 10X^2 + 1$ is reducible in $\mathbb{F}_p[X]$ for every prime number $p$, but it is irreducible over $\mathbb{Q}$. I am not sure how to approach this problem; any ...
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### Methods to show linear independence of functions, polynomials

There are apparently many methods to show that a set of functions are linearly independent. Forexample, there were some cases, where I saw use of derivative. At least to prove Lgrange polynomials are ...