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 radicals and the arithmetic tag. For questions about roots of Lie algebras, use the lie-algebra tag instead.

6663 questions

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3 answers

Solve $ \frac{1-\sqrt{1-x^2}}{1+\sqrt{1-x^2}} = 27\frac{\sqrt{1+x}+\sqrt{1-x}}{\sqrt{1+x}-\sqrt{1-x}}$. Is my solution correct?

Find the roots of the following equation, if any: $$ \frac{1-\sqrt{1-x^2}}{1+\sqrt{1-x^2}} = 27\frac{\sqrt{1+x}+\sqrt{1-x}}{\sqrt{1+x}-\sqrt{1-x}}. $$ My approach: The following constraints should hold jointly for x: $1-x^2\geq0\iff…

roots

asked Dec 10 '15 at 11:40

nullgeppetto

3,006

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2 answers

How to solve $e^x=kx + 1$ when $k > 1$?

It's obvious that $x=0$ is one of the roots. According to the graphs of $e^x$ and $kx + 1$, there's another root $x_1 > 0$ when $k > 1$. Is there a way to represent it numerically.

roots

asked Oct 14 '15 at 15:15

Chielo Newctle

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1 answer

Implication of two statements

my question is with regards to two different problems (both containing a statement A and statement B) that are quite similar. The objective is to decide how the implication arrow is supposed to be pointed (->, <-, <-> or not at all): A:…

roots

asked Sep 16 '15 at 22:37

gillon

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1 answer

is there a way to prevent false roots?

Is there a systematic way of preventing false roots when squaring a root equation? The testing of the roots is quite tedious in some problems. My first thought was absolute values in some form

roots

asked Aug 23 '15 at 18:56

user262493

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2 answers

What is the relationship between the concept of a square root and a number's prime factorization?

Essentially what I am asking is if there is some kind of correlation between a number such as √385 and it's factorization (which is 5,7,11). Is it possible to use a number's (especially very large ones) square root to help in finding out it's prime…

roots

asked Jul 15 '15 at 17:11

Jessiah Burgess

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1 answer

Discriminant with non-Real result

I have the following equation: $ ax^2 + (a+1)x - a = 0 $ Where $a$ is not $0$ When calculating the discriminant $\Delta$ i get a non-real result. But what does it mean? I know that a negative determinant denotes non-real roots.

roots

asked Mar 21 '15 at 14:07

jhuk

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1 answer

If $\tan\alpha,\, \tan\beta,\,\tan\gamma$ are roots of $au^ 3 +(2a-x)u+ y=0$

If $\tan\alpha,\, \tan\beta,\,\tan\gamma$ are roots of $au^ 3 +(2a-x)u+ y=0$ for fixed $x$ and $y$ and $\tan\alpha + \tan\beta = h$ Find $ah^3 +(2a-x)h$. Options are A) $y$ B) $-y$ C) $2a- x$ D) $a$ Solution We can find $h= - \tan\gamma$ But I am…

roots

asked Mar 14 '15 at 18:16

rst

2,031

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2 answers

How to solve a twin root equation?

I thought to factorize a sqrt(x), but I can't find out anything. I thought to multiply both sides with themselves four times, but I'm not sure that works.

roots

asked Feb 25 '15 at 18:09

user219242

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0 answers

Root with bolzano theorem

Given this equation $a\cos{x}+b=x$ with $a,b>0$ how to prove that there is at least one root between $(0,a+b]$ ? For $x=0$ its $a+b$ which is >0 For $x=a+b$ its $a\cos(a+b) -a=a(\cos(a+b)-1)\leq0$ The problem here is that it is less than equal not…

roots

asked Jan 27 '15 at 22:59

GorillaApe

1,071

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1 answer

Secant method and false position method exercise

We have $f(x)=x^2-6$. I have to find $p_3$ if $p_0 = 3$ and $p_1 = 2$ by using a) Secant method b) False position method So for the first one I have $p_2=p_0- \dfrac {f(p_0)(p_1-p_0)}{f(p_1)-f(p_0)}$= $3- \dfrac…

roots

asked Jan 04 '15 at 12:08

user3543012

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2 answers

Find root of equation using bisection method?

Question : Find an approximate value of $\sqrt[3]{25}$ using Bisection Method. Since it doesnt state the accuracy in the question,how many iterations am I going to do to get that approximate value? Also since it doesnt state the interval,how am I…

roots

asked Jan 03 '15 at 11:51

user3543012

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1 answer

What is meant by positive root of $x^3-x^3-1$?

I am a bit confused. I think there must be a mistake. In a text I read: The entropy is $2\ln p$, where $$p=\frac{1}{3}\left(\sqrt[3]{\frac{29+9\sqrt{31/3}}{2}}+\sqrt[3]{\frac{29-9\sqrt{31/3}}{2}}+1\right)$$ is the positive root of…

roots

asked Jan 03 '15 at 10:52

Salamo

1,094

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2 answers

How to calculate $\alpha '\beta '+\alpha '\gamma ' + \beta '\gamma '$ when finding roots for a cubic equation?

Given the roots of the cubic equation $x^3+4x^2+3x+2=0$ are $\alpha, \beta, \gamma$, determine the cubic equation with roots $\beta\gamma, \gamma\alpha, \alpha\beta$. How on earth do I work out what the value of $\alpha '\beta '+\alpha '\gamma ' +…

roots

asked Nov 04 '14 at 19:22

asa

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3 answers

Nature of roots of a quadratic.

Question: If the equation $x^2+2x+1+\lambda=0$ has real and unequal roots, determine the nature of the roots of the equation $(\lambda+2)(x^2+2x+1+\lambda)=2\lambda(x^2+1)$. My attempt: Taking $(\lambda+2)$ to the other side we have…

roots

asked Oct 31 '14 at 06:20

bibo_extreme

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0 answers

Find roots of $\sum_i \alpha_i\,\cos(\beta_i\,t)$

I'd like to solve analytically the following equation, where $\alpha_i$ and $\beta_i$ have known values in $\mathbb{R}$: \begin{equation} \sum_{i\leqslant N} \alpha_i\,\cos(\beta_i\,t)=0 \end{equation} Would there be an exact solution to this…

roots

asked Oct 06 '14 at 19:39

anderstood

3,504

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