Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [roots]

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 the (arithmetic) tag. For questions about roots of Lie algebras, use the (lie-algebra) tag instead.

Questions regarding values $x$, such that a function $f$ evaluates to zero at $x$. For questions about "square roots", "cube roots" and such, consider using the and the tag. For questions about roots of Lie algebras, use the tag instead.

6663 questions
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Solving for the zero of a multivariate

How does one go about solving the roots for the following equation $$x+y+z=xyz$$ There simply to many variables. Anyone have an idea ?
jessica
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Broyden's Method Failing to Converge

I have a matrix equation $$ \textrm{det}(\mathbb{M}) - \textrm{tr}(\mathbb{M}) + 1 = 0 $$ where $\mathbb{M}(z)$ is a matrix function of a complex number $z$ that I want to solve for. Because I have really two equations with two unknowns (real and…
webb
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Proof that the roots of a specific cubic equation are all real

I'm trying to prove that the cubic equation $_3 ^3 + _2 ^2 + _1 + _0=0$ has three real roots. The coefficients are $_3=−1−−−$ $_2=−2(++)$ $_1=(+)+(−3)$ $_0=2$ where each of , and are greater than zero. Applying the Rule of Descartes indicates…
Rich T
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Finding critical point between two roots

For finding a critical point like A ($f′(x(A))=0$) between x=α and x=β in $f(x)=(x-α)^m(x-β)^n$ I use this formula: $$x(A)=\frac{α.n+β.m}{m+n}$$ but I am interesting to know is there any formula like this to calculate the approximate or exact…
Behrang
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How can I get a square root of a number in Projective Line representation

In this Wikipedia article, I found the Projective Line: https://en.wikipedia.org/wiki/Projective_line. I want to know how to take a square root of a number in this representation. Let's take one example: the number $9$ is represented on projective…
aguiadouro
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Prove/Disprove that the asymptotes of a particular function always coincide with the extrema of a related function

I have a function that is real valued in the interval $x\in…
Sharat V Chandrasekhar
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Another way to proof $A^2=B^2$

When we have an eqaution in the form of $A^2=B^2$ the way that I've been taught would be to square both sides of the equation $\sqrt{A^2} = \sqrt{B^2}$ and the result would be that $A = B$ and $A = -B$ , but why is this the case? $A = B$ seems…
BroodjeRijst
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What is the root of $a(x) = 1 + x^r - 2(x-1)^r$?

I have been working on my thesis and I have stumble upon the following equation that is giving me a tough time: $$a(x) = 1 + x^r - 2(x-1)^r$$ What is the root of this equation? As in, for what values of $x$ will $a(x) = 0$? Is there a unique…
CobaltDev
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$-\frac{1}{2}z^{-2}+\frac{1}{2}z^{-1}+1=0$ How to determine values for z with negative exponents?

$-\frac{1}{2}z^{-2}+\frac{1}{2}z^{-1}+1=0$ For $\frac{1}{2}x^{2}+\frac{1}{2}x^{1}+1=0$ We could use the pq-Formula. I guess it is possible to use this here, but how? If not, what techniques are used for negative exponents? Tried use…
Rapiz
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What two values to five significant figures should I use for a sign change test to see that $1.228$ (4sf) is a root of $x^4+x^3-2x^2+3x-5=0$?

What two values to five significant figures should I use for a sign change test to see that $1.228$ (4sf) is a root of $x^4+x^3-2x^2+3x-5=0$? $$f(x)=x^4+x^3-2x^2+3x-5$$ $$f(1.2279)=-0.207149...$$ $$f(1.2281)=-0.205145...$$ $$f(1.3)=0.5731$$ The…
theonerishi
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Let $c$ be a positive real number for which the equation $x^4-x^3+x^2-(c+1)x-(c^2+c)=0$ has a real root $\alpha$. Prove that $c=\alpha ^2 - \alpha$

Let $c$ be a positive real number for which the equation $x^4-x^3+x^2-(c+1)x-(c^2+c)=0$ has a real root $\alpha$. Prove that $c=\alpha ^2 - \alpha$ I tried to to solve using relation between roots and coefficients but unable to progress much. Please…
Math-Learner
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Rouche's theorem: $g(z)$ has no roots in $L$, $|g(z)| > |f(z)|$ for the contour $\partial L$. Does $f(z)$ have no roots in $L$?

Let $f(z)$ and $g(z)$ be analytic functions. Let $L$ be the complex unit disc and its contour is $\partial L$, the complex unit circle $|z| = 1$. If $g(z)$ has no roots in $L$, e.g. $g(z) = z + 2$, and $|g(z)| > |f(z)|, z \in \partial L$, does that…
user60307
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Is $x=n^x$ solvable where $n>1$?

Since the graphs of $y=x$ and $y=2^x$ (or $y=n^x$ for that matter, where $n>1$) do not intersect, is $x=2^x$ unsolvable? Or is there some kind of a really clever way to find a root? P.S. I'm not too sure if this is the right tag to use.
user250486
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How to find a number when given the $n$-th root

If I am given something like $\sqrt[n]{100} = 10$ then it is obvious that $n=2$. But say I get something like $\sqrt[n]{2} = 36$; how do I find what $n$ is then?
user577111
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Rouche's theorem for two functions that have the same number of roots

I hope this is not too long. Thanks in advance! Edit: I edited it for a great deal, most of the information was unnecessary. Let us define a function $h(z) = f(z) + g(z)$. We know that $f(z)$ has $K$ roots for $z$ within the complex unit circle and…
user60307
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