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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Can we just ignore the negative value of a number or is there certain cases?

Q: If $x^2+\frac{1}{x^2}=7$, find the value of $\frac{x^6+1}{x^3}$. Given, $x^2+\frac{1}{x^2}=7$ $\rightarrow$ $(x+\frac{1}{x})^2=9$ $\rightarrow$ $(x+\frac{1}{x})=\pm 3$ Is it permissible to ignore $-3$ and use only $+3$ to find the value of…
Russell
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Proving that function has only one root

How to prove that the following function has only one root: $$f(x)= \frac{2x^2\ln(x)-x^2-8x}{4}$$ I tried with finding the second derivative and got $\ln(x)+1$. Now, since $\ln$ is an increasing function, the minimum is at $e^{-1}$. Then I tried to…
Trevor
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Number of roots of $f(x) = s f(x+B)$ for specific $f(x)$

For real function $f(x)=\frac{x^\beta}{1+\alpha x^\beta}$ with real $\alpha \ge 1$ and real $\beta>0$ I suppose that equation $$f(x) = sf(x+B)$$ for real $B$ with $0
athanasius
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How to solve equation analytically

The equation $$\int_{-\pi}^xt\sin(t)\,dt=1$$ is given. Calculating the integral and simplifying a bit, it reduces to the equation $$-x\cos(x)+\sin(x)+\pi-1=0$$ I've tried rewriting the trig functions using complex exponentials, but that got me…
Maj Zobrani
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roots of an equation modulo m

Proof, that the equation $$(x^2-13)(x^2-17)(x^2-13*17)$$ has no roots in $$\mathbb{Z}$$ but for every modulo $$m \in \mathbb{Z}_{\geq 2}$$. It is obvious that the equation has no solutions in $$\mathbb{Z}$$. I've already found out that the equation…
lisanno
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nulls of a function if out of domain.

I'm trying to find the nulls of $f(x) = \frac{x}{\sqrt{x^2+x}}$. I'd claim $f(x) \neq 0$ because it's not part of the domain. However by transforming: $f(x) = \sqrt{\frac{x}{x+1}}.$ So it can become $0$ zero somehow. However, does my claim still…
Leon
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Rational Root Theorem Help

today I found myself stumped on this problem: A polynomial with integer coefficients is of the form $$9x^4 + a_3 x^3 + a_2 x^2 + a_1 x + 15 = 0.$$Find the number of different possible rational roots of this polynomial. What I have: The possible…
random guy 2000
  • 139
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counting number of roots with Bolzano theorem

I have 2 Questions: How to get the roots of the equation f (x) = 0 using Bolzano theorem? (f is a continuous function and we dont know its type(polynomial or else)) How can the above algorithm be improved to count the number of double roots?
amz
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If $\alpha$ be a root of the equation $x^3+3x^2-6x+1=0$,prove that the other roots are $\frac 1{1-\alpha},\frac {\alpha - 1}\alpha$.

If $\alpha$ be a root of the equation $x^3+3x^2-6x+1=0$, then find the other roots. $\bf{Try}: $ I tried by using relation between roots and coefficients. Let $\beta, \gamma$ be the other two roots. Then $\sum \alpha =-3$ $ \sum…
Math-Learner
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Finding square roots of an unknown

$p$ and $q$ are rational numbers, find the values of p and q given that $2p = q \sqrt {76} + \sqrt {19}$ attempt: $$2p = 2q \sqrt{19} + \sqrt{19}$$ $$2p = \sqrt{19}(2q+1) $$ How to continue or how should I do?
Joe
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Problem with square roots and squares

Suppose we have $$ x^{2} = (-x)^{2}.$$ I understand that this equation holds because $$\begin{aligned} (-x)^{2} & = (-1\cdot x)^{2} \\ & = (-1)^{2} \cdot x^{2} \\ & = x^{2}, \end{aligned}$$ and so $\sqrt{x^{2}} = \sqrt{x^{2}}$ becomes $x = x$ and…
Tan2525
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Solving $x^{14} = 14^x$ for $x$

How can I transform the following equation: $$x^{14} = 14^x$$ to something of the form $$x = \cdots$$ Thanks!
David Meléndez
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Taking square roots in equations

When are we allowed to take square roots in an equation? For example, $x^2 = (x+2)^2$ Are we allowed to take square roots to solve it?
dugdugdug
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How to prove there is only one positive root?

If I want to prove $x^n+x^{n-1}-a=0$ has only one positive root for $a> 0$ and $n \ge 2$ Can I say for $n=2$ : $x^2+x-a=0$ and we know only one of the roots is positive. Now if we we know there is only one root for $x^n+x^{n-1}-a=0$ now I prove for…
justin Fo
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Deducing approximate root of equation

I'm working through a textbook and one of the questions is as follows: For $n$, $\epsilon$, and $\rho$ positive, consider the equation $n + \epsilon = z + ne^{-z/\rho}$. Expand the exponential term to third order and deduce that in the limit…
Derek Adams
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