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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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The validity of a solution with square root

So I had to solve this equation in my math book, $3x=\sqrt{18x + 72}$ the solutions I worked out are $x= -2$ and $x= 4$. Checking the validity of the solutions, for $x= 4$ gives $12=12$ and for $x= -2$ gives $-6=\sqrt{36}$ My correction book stated…
BroodjeRijst
  • 87
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What is the set of numbers that are roots of the exponential?

Usually when an equations has no roots it leads to a new set of numbers. For example $x^2+1=0$ lead to the development of complex and imaginary numbers. What are the extension of numbers that solve $$e^x=0\;?$$ Obviously this is not possible for…
Mauricio
  • 385
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why root 0 of 0 does not return error?

0 to the power of 0 is 0 multiplied 0 times by itself, a very illogical and twisted statement which returns error, but what about root 0 of 0, the calculator says 0. An example might help us: $2^3=8$ --> what is the result of multiplying $2 \times…
serax
  • 133
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Solution for approximating square roots?

I just saw a post on instagram which said that $$\sqrt{x}\approx \frac{x+y}{2\sqrt{y}}$$ I tried it out on a few values, and surprisingly, it came within 1 decimal point of the actual answer. Is there a reason for this or is it coincidental? y is…
prata
  • 215
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Find $r$ such that the equation $x^4+x^2(1-2r)-2x+1=0$ has only one real solution

I'm looking for $r$ such that the equation $$x^4+x^2(1-2r)-2x+1=0$$ has only one real solution. I've made some attempts to this problem, but it seems that I even didn't get close to the solution. The approximation for $r$ is 0.3347498 Is it…
Jakub Pawlak
  • 781
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Prove solution to $\sum\limits_{k=1}^{\infty}\frac{x^k}{x^{2k}-2x^k+1} = 0$.

Numerically I found a solution to the following equation at about $x = -0.4112$. $$\sum\limits_{k=1}^{\infty}\frac{x^k}{x^{2k}-2x^k+1} = 0 \quad x \in \mathbb{R}, -1 < x \leq 0$$ Now, I want to get the exact proven solution. I know that I can…
thinkingeye
  • 399
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3 answers

Solving $\sqrt{x}-2\sqrt[4]{x}-8 = 0$

How can I do this question? $$\sqrt{x}-2\sqrt[4]{x}-8 = 0$$ Can I solve this? I tried to multiply everything by $x^4$, and got $$8x^4+x^3 -2x = 0$$ I don't know how to proceed from here.
user69840
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Roots in equation

In the equation $\sqrt{x-2} - \sqrt{6x-11} + \sqrt{x+3} =0$ I got the roots of $x$ being $6$ and $7\sqrt{3}$. Considering the graph shows only $6$ as being a valid solution, how should I go as figuring this out in the equation itself?
KumaCat
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Find the roots of equation based on some geometry hints

Plots of the equations $y = 8 - x^2$ and $|y|=\sqrt{8+x}$ are symmetric w.r.t. the line $y=-x$. We have to solve the equation $$8-x^2=\sqrt{8+x}$$
user678243
2
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2 answers

Find the solutions of the equation

$x^3- 3x + 2 = 0$ Using the Horner scheme, I can find easily the roots of the equation: $x_1 = x_2 = 1 $ and $x_3 = 2.$ How can I find them using other method ?
Florin M.
  • 635
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1 answer

Solution of $\omega_4 z^4+\omega_3 z^3+\omega_1 z+\omega_0=0$

Let us consider $$\omega_4 z^4+\omega_3 z^3+\omega_1 z+\omega_0=0\quad (1)$$ where $\omega_0,\omega_4>0$, $\omega_1,\omega_3\in\mathbb R$ ($\omega_1,\omega_3$ both negative or both positive). Let us consider the following situations: All the roots…
Mark
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Find the value of "n" in terms of "a" when $\sqrt[n]{a+{\sqrt[n]{a+{\sqrt[n]{a+{\sqrt[n]{a+\cdots}}}}}}} = a$

I saw on the internet that $\sqrt{2+{\sqrt{2+{\sqrt{2+{\sqrt{2+\cdots}}}}}}} = 2$ I want to find a solution for n in terms of "a" for a general formula $\sqrt[n]{a+{\sqrt[n]{a+{\sqrt[n]{a+{\sqrt[n]{a+\cdots}}}}}}} = a$ , $a\in\mathbb{R_{>0}}$ Here…
Larry
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Find explicitly the positive solutions of $2^x=x^2$

Find explicitly the positive solutions of the equation $2^x=x^2$ I noticed that $x=2$ and $x=4$ are roots of the equation. How can I prove that they are the only positive ones? Thanks in advance
Lorenzo B.
  • 2,252
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show that the equation has a root in the interval $(0, \pi)$. And the question didn't mention that its continues.

show that the equation has a root in the interval $(0, \pi)$ $$e^{x/\pi} + \sin(x) = x^2$$ I have solved it with the Intermediate Value Theory (as below) but I don’t think that my justification is enough, and I don’t know how to do it in a different…
Abdulrahman Alattas
  • 79
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Using the duplex method to calculate square roots

I have been assigned to find out how a calculator figures out square roots, so far the shortest thing I can see is "the duplex method". But the thing is that the explanation on Wikipedia makes no sense for me: " Find the square root of…
user115422
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