# Tagged Questions

Questions about the set of values at which a given function evaluates to zero. For questions about "square roots", "cube roots", and such, consider using the (radicals) and (arithmetic) tag. For questions about roots of Lie algebras, use the (lie-algebra) tag instead.

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### Am I thinking about the Argument Principle in the correct way?

I know that, by the Argument Principle, the number of zeroes of a function f inside a simple closed contour $\gamma$ minus the number of poles inside $\gamma$ = the number of times that the image ...
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### How to compute the argument of z= i(y^5+3y)+1,

I'm trying to find the number of zeroes of $z^5+3z+1$ in the first quadrant. I've already shown that there are no roots along the half lines -- the boundary -- of the first quadrant. Now I want to ...
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### The polynomial $a z^n+z+1$ has at least one root in $|z| \leq 2$

I am trying to solve this problem, but I don't have any idea. The problem is: Prove that for arbitrary $a \in \mathbb{C}$ and $n \geqslant 2$, polynomial $P(z) = a z^n+z+1$ has at least one root ...
Prove or disprove that for positive coefficients: $$a_k>0$$ this polynomial: $$a_1x^0+a_2x^1+a_3x^2+a_4x^3+...+a_nx^{n-1}-x^n=0$$ has a real root $x$ that is the fraction from the following ...