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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No. Of real roots of an equation

Consider the function $$ f(x) = 2\cos((x^2+x)/6) - 2^x - 2^{-x}. $$ Clearly $x= 0$ is a root of equation so number of real roots can not be 0 but how to figure out question how many ? From where does this observation start?
Gopesh Thakur
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Why isnt this value imaginary? Or is it?

Lets suppose we have a square, 50m², and another square, 25m². Subtracting the second from the first we get: $$50\textrm{m}^2 - 25\textrm{m}^2 = 25\textrm{m}^2$$ something that makes absolute sense, so why cant we say that 5m could make up a…
Charlie
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Finding real roots of $f(x) = 4x^5 + x^3 + 7x - 2$

$$f(x) = 4x^5 + x^3 + 7x - 2$$ $f'(x)>0$ for all $x$, But $f''(x)=80x^3+6x$ can be negative for negative $x$, so is the function strictly increasing?
onelessproblem
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How to solve $\pi\sin^2x-\sin^22x=0$?

By use computer, I know it has a solution in $(0,1)$, but I don't how to get it .
Enhao Lan
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Find root of equation $\frac{2bnx}{a\sqrt{x^2-b^2}}+\frac{2bx}{a}+\frac{2ax}{b}-2m=0$

How I can find $x$ for this equation $$\frac{2bnx}{a\sqrt{x^2-b^2}}+\frac{2bx}{a}+\frac{2ax}{b}-2m=0$$ where $a, b, m, n$ are constant numbers. Thanks.
a hidayat
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How to find all solutions for $x^3=6x+6$

Could anyone help me to find how to find all solution for $x^3=6x+6$?
Myshkin
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How to show $\frac{1}{\lambda}(z-x)+\ln z = 0$ with $\lambda >0$ has a positive solution $z$ for any $x$?

How to show $\frac{1}{\lambda}(z-x)+\ln z = 0$ has a positive solution $z$ for any $x$? It seems no problem $z>0$ because of the $\ln(\cdot)$ function. However, how to show there exists an solution for this equation? I use the method such as…
sleeve chen
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Possible values of a parameter in an arithmetic progression

In the following question . How do they get to know that the possible values of $a$ are only $3$ and $4$?
Koolman
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Why is the sum of the roots of $x^3+9=12x$ zero?

I found the roots of the equation to be $$x=3,\frac{\sqrt{21}}{2}-\frac{3}{2},-\frac{\sqrt{21}}{2}-\frac{3}{2}$$ Algebraically, why is the sum of these roots equal to zero?
Citut
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Could 1/0 be an imaginary number?

There is no way to find the square root of a negative number. It just doesn't work. So the answer to the impossible question, "What number squared equals a negative number?" is just said to be $i$, an imaginary number. So now let's look at a…
NoRt9001
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Method to find $(x_1, x_2,...,x_n)$ s.t. polynom $p(x_1, x_2,...,x_n) \bmod m = 0$

I have a natural number $m$, and a polynomial $p: \mathbb{Z}^n \rightarrow \mathbb{Z}$, and I need to find a set $(x_1, x_2,...,x_n)$ so that $p(x_1, x_2,...,x_n) \bmod m = 0$. First: Does every non-constant polynomial have such a set? And more…
Mike B.
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find number of real roots

The number of real roots of the equation $$2\cos((x^2+x)/6) = 2^x + 2^{−x}$$ My approach: If I put $x=0$ in both side then $LHS=RHS$ so one real solution is zero but I'm not able to find if it has any other real root or not
Sourasekhar Banerjee
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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.
unicornki
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Set of solutions to $\sqrt{x^2}=-x$

The question is: The set of all real numbers x such that $$\sqrt{x^2}=-x$$ consists of: A: zero only B: nonpositive real numbers only C: positive real numbers only D: all real numbers E: no real numbers I chose D because the root of any number…
dngr193
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Proving Sum of Roots is Zero

The question is if $w$ is any real number , the equation $z^k = w$ has $k$ roots, $k ∈ n$. Show that the sum of the k roots is zero. Usually with these root questions I convert the right hand side to polar form so in this case $z^k = w cis 0$ $z =…
bigfocalchord
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