# 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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### 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....
279 views

### 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 ...
38 views

### Are minimizing a function and root finding the same?

What is the relationship between minimizing a function and finding a root of an equation? Are the the same? I know in both problem we have similar algorithms, such as gradient decent, or newton's ...
39 views

### 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?
55 views

### 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 ...
32 views

### 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 ...
20 views

### 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: $P[λ]$ = $λ^5$ - $563/315λ^4$ + $0.3476λ^3$ - $0.0038λ^2$ ...
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### Restrictions on the coefficients that allow a polynomial in a field of characteristic 0 to be solvable by radicals and the associated formula.

Given a field $F$ of characteristic $0$, we know that a general polynomial $p(x) \in F \left[ x \right]$ is not solvable by radicals if $n \geq 5$. However, I was wondering what restrictions can one ...