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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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Does $5\sqrt{5}\div5\sqrt{5}$ equal 5 or 1

Does $5\sqrt{5}\div5\sqrt{5}$ equal $5$ or $1$. I think it is $1$ but I just want to check I have not missed anything.
dagda1
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How could I better represent the multiplicity of a zero of an equation?

Context If I have an equation which factors to $(x-2)(x-2)(x+3)$, the zeros are 2, 2, and -3. The multiplicity of the zero "2" is 2 because it occurs twice. In graphing this equation, the multiplicity is visually represented by the graph either…
MJMarquez
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What does "$f(x)$ has a root of order $k$" mean?

I'm confused by the wording of this, the question states: Assume $f(x)$ has a root of order $k=3$ at $x(n)$. What does the "root of order $k=3$" part mean? Thanks
itofu55
  • 19
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Roots of the equation $x^3+15x^2+cx+860=0$

If $-5+i\beta$ , $-5+i\gamma$ ,$\beta^2\ne\gamma^2$; $\beta,\gamma \in R$ are the roots of the equation $x^3+15x^2+cx+860=0$, $c\in R$, then find the three roots of the equation. My approach is as follow, It is mentioned that the roots are not…
Samar Imam Zaidi
  • 8,800
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Find the roots of $f(x) = 2\cos(x)$

From a book I know that the roots of $\cos(x)$ are: $$\left[\ldots,-\frac{3\pi}{2},-\frac{\pi}{2},\frac{\pi}{2},\frac{3\pi}{2},\frac{5\pi}{2},\ldots\right]$$ What are the roots of $2\cos(x)$? I have the answer…
Doug Fir
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Get all roots of a 6th degree polynom numerical

I have a polynomial of the 6th degree. For this Polynom, I want to get all real roots. My problem is that all the Methods I read about are only to get one root. Is there a way how I could get all the roots? For example: With a polynom of 5th…
IlPad
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Square Root Function Breaking Rules?

There is a rule that if a function is not one to one, then its inverse is not a function. When graphed, a quadratic function is not one to one. However, there is also a rule that the square root and radical sign with the default index of 2 only…
Hello World
  • 163
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How to simplify cubicle numbers?

I have been stuck on a question in my math book for days and I have tried every website and video on youtube but none of them were helpful. There's a cubicle number as 3 radical 54 which simplifies, according to my guide book, to cubicle number 9…
mathquest3324
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Roots of a equation

Let $t\geq 0$, $p\in(0,1/2)$, $q=1-p$ fixed and consider the equation $$t=\frac{1-x-\sqrt{(1-x)^2-4 p q}}{(1-x) \sqrt{(1-x)^2-4 p q}-(1-x)^2+4 p q}.$$ How can I get the $x=1\pm\sqrt{4 p q + t^{-2}}$?
Avertere
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Finding solution by solving $x^3+1=0$

It is easy to solve $x^3-1=0$ by having the form $(x-1)(x^2+x+1)=0$ The $3$ roots are: $x=1$, $x=\frac{-1\pm i\sqrt 3}{2}$. But, solving the equation $x^3+1=0$ by using the similar approach of using the standard approach to solving the quadratic…
jiten
  • 4,524
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Calculus - Interval Bisection Method

For x^5-x=3, explain why there must be a zero of the function between (0,2). I know that I should use the intermediate value theorem to prove this, but I can't think of a good way to explain this.
J-Dorman
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Calculate high-order roots by hand

Say you were asked to calculate a high-order root by hand. For example, the 13th root of 230,120,000 to 4 significant digits. How would you do it? Would you do a manual Newton-Raphson iteration? Or perhaps a more crude sequence of repeated guessing?…
oz1cz
  • 171
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Root finding when QR decomposition doesn't work

I searched for a root finding algorithm and found QR decomposition with Companion matrix which was promising but I found a couple equations where this method didn't work. These for example won't be solved:$$ x^4 - 10x^2 + 9, \quad x^3 - 5x^2 - 4x +…
FROST SKIPPER
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2 answers

Sum of roots of equation

For k > 0, the set of all values of k for which $$ke^x - x = 0$$ has two distinct roots is (a, b/c), such that b/c is in its lowest form, then what is the value of a + b + c?
user3701522
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Smallest positive integer solution

I am new to Abstract Algebra, and in the 5th edn. of the book by Hillman, Alexanderson have come across the below question #25 in section 1.2. For each of the following integers d, find the smallest positive integer n such that $d|(10^{n} -…
jiten
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