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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Number of real solutions of $f(f(f(x)))=1$, where $f(x) = x-x^{-1}$

given $f(x) = x-x^{-1}$ ,then number of real solution of $f(f(f(x)))=1$ $f(x)=\frac{x^2-1}{x}$, $f(f(x))=\frac{(f(x))^2-1}{f(x)} = \frac{(x^2-1)^2-x^2}{x(x^2-1)}=\frac{x^4-3x^2+1}{x^3-x}$ $f(f(f(x))) = \frac{(f(x))^4-3(f(x))^2+1}{(f(x))^3-f(x)} =…
Girish Pimoli
  • 55
2
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3 answers

The roots of $x^n - 1=0$?

Obviously, $x=1$ is one of the roots. There must be other roots who are complex number. I guess they are related to exponent. I don't know how to get them and how to prove it.
You_Don't_Know_Who
  • 706
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0 answers

Does $x^a + bx + c = 0$ have an analytic solution?

Does $x^a + bx + c = 0$ have analytic solution given $a \in \mathbb{R}, a > 1$ and $x > 0$? The case that I am interested also has $b < 0$ and $c < 0$. Searches have led me only to the quadratic formula, and to the the form $a^x + bx + c$, so…
Ott Toomet
  • 121
2
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7 answers

Algebraic solution of complex equation

For solving algebraically any complex equation involves two components for the real & imaginary parts. Let the real part be - $a$, imaginary part - $b$. For the complex equation $$x^3 = 1-i $$ Substituting $x = a +bi$, we get: $$(a+bi)^3 = 1 -…
jiten
  • 4,524
2
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1 answer

Is the Square Root of a Real Number both positive and negative?

Is the "Square Root of 4" equal to ±2 or 2? And the twist here is that if it is equal to ±2, then, what is "√4 + 2"? Is "√4 + 2" equal to just "4", or "4 and 0"? I am studying root right now and I just cant figure it out.
WhatsYourIdea
  • 123
2
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2 answers

How to find the number of solution pairs for this equation?

Question: Consider the equation $(1+a+b)^2=3(1+a^2+b^2)$ where $a$ and $b$ are real numbers. How many solution pair(s), ($a$,$b$), are possible for this equation? My attempt:…
MrAP
  • 3,003
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0 answers

Describing roots as equations?

If we look at the equation $xy=0$, the roots of that equation can be described as two linear equations: $x=0$ and $y=0$. It seems to me that there must be other equations where the roots can be described as higher order curves, and possibly even…
Alan Wolfe
  • 1,259
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2 answers

Find sum of roots squared

If $α$, $β$, $γ$, are the roots of the equation $x^3-5x+3=0$, find the value of $α^2+β^2+γ^2$. Im stuck on this question for a while now, please help me with explanations, thank you very much!
2000mroliver
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Prove that $\frac{x^3}{3}-\sin x-x=0$ has only one positive root?

I need to prove that this equation $\frac{x^3}{3}-\sin x-x=0$ has only one positive root. How can I do that?
Afnan
  • 29
2
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2 answers

Is it possible to solve sin(x) - $\frac{1}{x} = 0$ for x analytically?

I was wondering how I might go about finding the roots of this equation? Can it only be done using root approximation methods like newton's method?
user373763
  • 85
2
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2 answers

Which is bigger and how to check?

I have $\dfrac{20\sqrt3-23}3$ and $\dfrac{\sqrt6+12}3$ but I don't know how to check which is bigger and which is smaller. Can someone help me?
Dimsn Uzunov
  • 21
2
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1 answer

How to approximate the order of a root given the base and the power

I need to narrow the range (minimum/maximum) to search for a root given the base and the power, the values are all integers, the base can be very large relative to an always positive power. Is there a quick way to determine the order of the root…
slashmais
  • 223
2
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0 answers

Finding all complex roots of an equation with exponentials.

I know that $$ (-1)^x + 2^x - 2 x - 1 = 0 $$ has a single real root $(x =3)$ and an infinite number of complex roots whose real part appears often negative. Don't the complex roots also have their conjugates as solutions(roots)? Even I am unable…
Narasimham
  • 40,495
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2 answers

How to find $x$ when $2^{x}+3^{x}=6$?

$$2^{x}+3^{x}=6$$ How to find the real number x? I mean it's approximately $1.19$ bur can we write $x$ as the form of $a, b, c$ when $a^{x}+b^{x}=c$ in general. Maybe an infinite sum?
esege
  • 3,621
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how to find the roots of the following floor-equation:

How to find the roots of $$\lfloor x\rfloor+\lfloor 2x\rfloor+\lfloor 3x\rfloor=6$$
d.v
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