# 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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### Why this book says that $2^{1/2} = ±\sqrt{2}$?

Shouldn't it be: $2^{1/2} = \sqrt{2}$ ? I know the problem is that there they are working with complex numbers, but I still don't understand. The book is in the link, page 113, when they move ...
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### Real solutions of $x^5+ax^4+bx^3+cx^2+dx+e=0$

If $2a^2＜5b$,prove that the equation $x^5+ax^4+bx^3+cx^2+dx+e = 0$ has at least one complex root。Thanks.
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### Can we permute the coefficients of a polynomial so that it has NO real roots?

Let $P(x)=a_{2n}x^{2n}+a_{2n-1}x^{2n-1}+\ldots+a_{0}$ be an even degree polynomial with positive coefficients. Is it possible to permute the coefficients of $P(x)$ so that the resulting polynomial ...
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### Mental $n-$th root of $N$

It has been a while since I started thinking about this problem: a fast method to evaluate (in an approximate way) mentally the $n-$th root of a number $N$. I'm talking about great numbers, because ...
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Using the roots of $z^5=1$, or otherwise, write $z^4+z^3+z^2+z+1$ as the product of two quadratic expressions with real coefficients. Hence find the exact value of the product $\cos(2\pi/5)\cos(4\pi/5)... 1answer 54 views ### Zeros of analytic function accumulating to the boundary By$\mathbb D$denote the open unit disc in$\mathbb C$. Suppose that$f : \overline{\mathbb D}\to\mathbb C$is analytic on$\mathbb D$and continuous on$\overline{\mathbb D}$. Assume now that there ... 2answers 50 views ### Finding number of roots using Rolle's Theorem, and depending on parameter I need to count the number of real solutions for$ f(x) = 0 $but I have an$m$in there. $$f(x) = x^3+3x^2-mx+5$$ I know I need to study$m$to get the number of roots, but I don't know where to ... 0answers 60 views ### Does there exist a closed form expression for roots of polynomials of the form$x^n + bx + c$Where$n \in \mathbb{N}$.$n$need not be less than five. 2answers 71 views ### Matlab Newton-Raphson for x-tan(x) For the function$f(x)=x-tan(x)$I am trying to find the 3 smallest roots to six decimal places. Attempt: We need to use an iterative method to solve this problem, and I choose to use Newton-Raphson ... 2answers 118 views ### Why is the sin of n times pi always 0 My instructor says that$\sin(\pi \cdot n)$is always equal to$0$. However, when playing with jsconsole.com, I find that this is not the case. ... 2answers 671 views ### Prove that all roots of$\sum_{r=1}^{70} \frac{1}{x-r} =\frac{5}{4} $are real Prove that all roots of $$\displaystyle \sum_{r=1}^{70} \dfrac{1}{x-r} =\dfrac{5}{4}$$ are real I encountered this question in my weekly test. I tried setting$\displaystyle \sum_{r=1}^{70}...
I would like to solve an equation of this type: $$A-BK_0(\kappa r)-CK_1(\kappa r)=0\ \ \ \text{with}\ A,B,C,\kappa\in\mathbb{R},\ \text{known}$$ i.e. I am looking for the zeros of the l.h.s. I am ...