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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Guessing bounds for the roots of a function, and counting roots within those bounds

In my book, it's written that we can guess how many roots an equation might have and where they approximately are by its graph or the table of function values without trying to solve it. There's an example afterward, doing that for $f(x)=\sin x -x…
Gigili
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Prove the number of solutions a function has?

What methods/theorems are commonly used when trying to prove that a function has exactly one root within a given interval $(a,b)$, or that it has no roots? I have the function $f(x)=\dfrac1x-\dfrac{\cos x}{\sin x}$. It is a strictly increasing…
Mother
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How to prove a nonlinear tracendent equation has two positive roots?

How to show (but do not use numerical software such as Mathematica, Matlab...etc.) that this equation \begin{equation} \frac{u (83811 u-88223)+18076}{396-3276 u}-\frac{10 \log (u)}{3}-\frac{1}{2} \log \left(\frac{98 u+14}{273 …
LCH
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are all polynomial equations solvable

Has anyone read the Book named " Monad science" published by Lambert Academic Publishing on 28 Febuary,2014 …
Hashir Omer
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How many solutions to $f'(x)=0$

How many solutions to $f'(x)=0$, when $f(x)=(x-1)(x-2)...(x-n)$ I know that $f$ is a polynomial of degree $n$, so $f'$ has at most $n-1$ roots It depends on whether $n$ is odd or even ? Thanks
TomM12
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Integer root of an equation

I saw this question somewhere, have a doubt whether it's correct. Suppose $a_1, a_2 \cdots a_{2n}$ are distinct integers. The equation $(x-a_1)(x-a_2)...(x-a_{2n})-(-1)^n(n!)^2$=0 has an integer solution $r=(a_1+a_2...+a_{2n})/2^n$.
UNM
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Roots of a given equation

How can I show that the equation $$e^x-\ln(x)-2^{2014}=0$$ has exactly two positive roots?
liesel
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Finding Roots of 2 Variable Inequalities

If I happen to have a two variable inequality such as $x+y
jessica
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Finding the roots of this function

I have the following special function. $$f(x) = \sum _{i=1}^n \left\{\frac{(x - z_i)_+^2}{1+ 2*z_i+(x - z_i)_+^2}\right\} - \left\{(\frac{x^3}{3} - \frac{(x - z_i)_+^3}{3})\right\} $$ which + means If $z_i$ is bigger than x its equal $z_i - x$ and…
rose
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Roots of sums of functions

Suppose a function $$ g(x) = a\cdot q(x) + b\cdot f(x) $$ where $q(x)$ is an arbitrary quadratic function, $f(x)$ is an arbitrary function that's decreasing and $f(x) \leq 0$ for all $x$. Is it possible to show that $g(x)$ only has 0,1,or 2 roots?…
NavStoke
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Proving the existence of a root, with an unidentified f(x)

I have the following problem: f(x) is a polynomial function. Prove that the equation: g(x)=tan(x)-f(x) has a root (so g(x) = 0). I considered the limitations of tan, and tried to get some values to apply the intermediate value theorem but the…
Math Horse
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Mathematical notation for repeating an equation

I wanted to write a way of calculating a square root of a number in LaTeX. Unfortunately, as a beginner in this sphere, I do not know what math symbol means to repeat the process. To make it clear, here is my equation for finding a square root of a…
Sarich
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Solve equation $4 \sqrt{1-x} = x+6-3\sqrt{1-x^2}+5\sqrt{1+x}$

I have some difficulties with this problem: Solve the equation: $4 \sqrt{1-x} = x+6-3\sqrt{1-x^2}+5\sqrt{1+x}$ I tried to let's $\sqrt{1-x} = a$ and $\sqrt{1+x}=b$ then try to solve equations but it seems difficult. Can anyone help me deal with this…
Jnote
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solving the amortization formula for i

Trying to solve the loan amortization formula $a=\frac{pi}{1-(1+i)^{-n}}$ (https://en.wikipedia.org/wiki/Amortization_calculator) for $i$, the interest rate per period. Have tried root solver on excel to no avail. Any help would be much appreciated.…
iHaveAQuestion
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Bodmas and square root evaluating curiosity

When evaluating a problem where there is a square root, should I assume that the square root falls under the order part of bodmas?
General raid
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