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
0
votes
1 answer

Prove that area of non-shaded region is 16+8√3-6π

The radius of circles is √2. Prove that area of non-shaded region is 16+8√3-6π I can't solve this at all... I can do the three circles area which is 6π, but can't get the rectangular height. https://i.stack.imgur.com/T5I9E.jpg Sorry about the…
Yves Bonneau
  • 5
0
votes
2 answers

$0$ as valid solution

In the equation $\frac {4}{x+ \sqrt{x^2+x}}-\frac {1}{x- \sqrt{x^2+x}} = \frac{3}{x}$ is $x=0$ considered a valid solution? The other one being $x=\frac{9}{16}$. After all, if $x=0$ the whole equation ends as $0=0$.
KumaCat
  • 67
0
votes
2 answers

Square Root Simplifying and Solving the problem to X

$e^y = \frac{x}{a} + \sqrt{( 1 + (\frac{x}{a})^2}$ The problem asks to solve this equation to x. My problem stands still by the square root.
Ilgaz Kuscu
  • 11
0
votes
5 answers

Why can you not square each individual term in an equation like $\sqrt{11} +\sqrt{44}= \sqrt{99}$?

Given the equation $\sqrt{11} +\sqrt{44}= \sqrt{99}$ Why is squaring each individual term not allowed? Doing so we get 11+44=99 which is incorrect. Is it because $\sqrt{11} +\sqrt{44}$ is considered a term grouped by addition and therefore to be…
Sphygmomanometer
  • 231
0
votes
1 answer

Value of the First derivative at the roots of a polynomial

For a polynomial $ f: \mathbb{R} \rightarrow \mathbb{R} $, $$ f(x) = c - \sum_{k=0}^n x^k $$ where $ c \geq 0 $ I would like to find the value of $ f'(x) $ for all the roots $ f(x) = 0 $, for Dirac Delta composition. I haven't been able to get very…
user178563
0
votes
1 answer

Finding zeros in a goniometric function

I need to find the zeros (roots?) of a function e.g. $$x-\sin(2x)$$ in the interval $[0,\pi]$ so that would make $$\sin(2x) = x$$ I've already found $0$ but I can't find a way to determine the other one
Wouter Vandenputte
  • 233
0
votes
2 answers

The range of constant $k$ for which all the roots of equation $x^4+4x^3-8x^2\:+k\:=0$ are real.

The range of constant $k$ for which all the roots of equation $x^4+4x^3-8x^2\:+k\:=0$ are real. Options a) $(1,3)$ b) $[1,3]$ c) $(-1,3)$ d) $(-1,3] $
raghav rajput
  • 19
0
votes
2 answers

How to solve the following square root?

I'd like to know how to solve the following square root:- $\sqrt{4+4x}$ The result is: $2\sqrt{x+1}$ I did not understand where the $x+1$ come from.
Mark Cunnighan
  • 9
0
votes
2 answers

New roots from old

The roots of $2x^2 − 8x − 1$ are $\alpha$ and $\beta$. Suppose another quadratic, $x^2 + qx + r$, has roots $1/(\alpha^3\beta)$ and $1/(\beta^3\alpha)$. What are $q$ and $r$? What I did to solve this question was $-q = (\beta^2 +…
user639649
  • 395
0
votes
1 answer

How can I find the roots of this for k?

$$ln(1-e^{-kx})(1-e^{-kx})+kxe^{-kx}=0$$ I need to find $k$ in this equation , it should be a function of $x$. Any hints on how should I do it ?
oren revenge
  • 566
  • 4
  • 13
0
votes
3 answers

Find all values of $a$ for which equation $ e^{x^2} = ax$ always has exactly two roots.

How shall I solve the following question? Please help! "Find all values of '$a$' for which equation $ e^{x^2} = ax$ always has exactly two roots."
HeetGorakhiya
  • 17
0
votes
1 answer

Checking for real roots of an even-th degree polynomial $ (a-x)^{2n+1}+x^{2n+1}-b=0 $

How should one check for real solutions of an even-th degree polynomial similar to this $ (a-x)^{2n+1}+x^{2n+1}-b=0 $ ? a, b and n are constant non-zero natural numbers
Matei Radu
  • 23
  • 5
0
votes
1 answer

Finding roots with Newton's method

I have $$ f(x)=x^7-12 $$ and need to find the roots with $\epsilon=0.0001$ accuracy. I have done the first steps but can't continue further. Here's what I've done: Ive narrowed down the range where I there is a root and found those $x$…
user3132457
  • 391
0
votes
2 answers

$p^3+q^3+r^3$, where $p$,$q$, and $r$ are the roots of the cubic function $x^3+4x^2-4x+1$. Working included.

I am trying to utilise the expressions for Vieta's fomulae to solve expressions, just as an investigation. The question I gave myself is, if $p$, $q$, and $r$ are the roots of a cubic, what is $p^3+q^3+r^3$? The cubic is $x^3+4x^2-4x+1.$ I have…
Chem_Student
  • 3
0
votes
1 answer

Solutions of $\cos(ax^c + bx) = 0$

As per title, I would like to find the zeros of $$ f(x) = \cos(ax^c + bx)$$ where $0\leq x \leq K$, $a \in \mathbb R$, $b \in \mathbb R$, and $c \in (0, 2]$. I have that $$ f(x) = 0 \Leftrightarrow ax^c + bx = \pi \left(n - \frac{1}{2}…
user126540
1 2 3
…
20 21