# 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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### Symmetric roots of polynomial

Let $\alpha_1, \alpha_2, \alpha_3$ be the roots of the polynomial $x^3 - x^2 + 2x - 3$ $\in \mathbb{C}[x]$. Calculate $\alpha_1^3 + \alpha_2^3 + \alpha_3^3$. What to do here exactly? I already ...
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### How to find the roots of this 4th order polynomial?

Can someone explain how to factor/find roots to this 4th order polynomial: $$s^4 + 14s^3 +45s^2 +650s + 1800 = 0$$ It's such a nightmare. I've been stuck for hours, any help would be appreciated :)...
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### Find the algebric form of the zeros(roots) of the following polynomial: $\left(\:z^2+iz+2\right)\left(z^3-8i\right)$

Good morning to everyone. I don't know how to find the zeros(roots) of the following polynomial function: $$\left(\:z^2+iz+2\right)\left(z^3-8i\right)$$. What I've tried: The zero(root) of the second ...
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### Show the roots of the quadratic equation $z^2 +bz+ c = 0$ lie in or on the unit circle

So I need a little help with the following: Considering separately the cases of real and complex roots show that the roots of the quadratic equation $z^2 +bz+ c = 0$ lie in or on the unit circle (i.e....
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### Why Rational Root Theorem only works with integers

Why does the rational root theorem only work when the polynomial has integer coefficients?
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### Factoring polynomials when roots are external to the ring

I shall avoid maths script since I'm typing on a mobile, anyway I think I can do without. I have a question about factoring polynomials over a ring. Let's call R the ring in question. It is clear to ...
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### Which is bigger and how to check?

I have $\dfrac{20\sqrt3-23}3$ and $\dfrac{\sqrt6+12}3$ but I don't know how to check which is bigger and which is smaller. Can someone help me?
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### Solving $2x^4+x^3-11x^2+x+2 = 0$ [duplicate]

I am having no idea how I can solve this problem. I need help! Here's the problem $2x^4+x^3-11x^2+x+2 = 0$ I am learning Quadratic Expressions and this is what I need to solve, and I can't ...
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### Understanding a calculation deduced for the function $\pi^{-s/2}\Gamma(s/2)\zeta(s)$

With my current knowledges I don't know if this is a bad question, but since I am interesting in this kind of calculations I want to ask you, if I was wrong or if if my statement is obvious. From ...
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### Specific fucnction has 11 different zeros

Let $f : \mathbb{C} \to \mathbb{C}$ be given by $$f(z) = z^{11} + 4 e^{z + 1} - 2$$ Show that $f$ has 11 different zeros in the annulus $\{z \in \mathbb{C} : 1 < |z| < 3\}$. This is an old ...
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### Solving a characteristic Polynomial of the Hilbert Matrix

I need to find the eigenvalues of the following characteristic polynomial but I can't seem to successfully find the roots of the equation: $P[λ]$ = $λ^5$ - $563/315λ^4$ + $0.3476λ^3$ - $0.0038λ^2$ ...