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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1 answer

New roots from old quadratic with coefficient p

The roots of $−2x^2 + x + 4$ are $α$ and $β$. Suppose another quadratic, $px^2 + qx + r$, has roots $α +1/β$ and $β + 1/α$ What is the form of the new quadratic? To solve this I got that $α+β=1/2$ and $αβ=-2$. After doing so I end up with; $q/p =…

roots

asked Apr 25 '19 at 02:36

user639649

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2 answers

Use Intermediate Value Theorem to prove $\sqrt{s}$ exists, for $s>0$

I'm self-studying proof theory, and working on the following problem: Consider $s\in\mathbb{R}$, with $s>0$. Apply the Intermediate Value Theorem to prove the existence of $\sqrt{s}$. I figure I can use the theorem to prove the existence of a root…

roots

asked Feb 23 '13 at 18:58

ivan

3,237

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1 answer

Finding the limiting cases for the root of a function

I'm sorry my title is not descriptive; the function I am interested in is too long to put in there. What I am looking at is the roots of the following function: $f(\epsilon) = (\Delta^2-\epsilon^2)(\epsilon^2 - (\Gamma_1+\Gamma_2)^2/4) + \Delta^2…

roots

asked Feb 16 '19 at 15:42

user3183724

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2 answers

The root sign and it's relation with 1/2.

$\sqrt{4}=2$ But is it same as writing... $4^{1/2}=2$? Basically I do not understand why $\sqrt{}$-sign equals $1/2$?

roots

asked Aug 11 '18 at 04:48

Saksham Sharma

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1 answer

Descartes principal imaginary roots

If $\ a_1,\ a_2,\ a_3,...\ a_n$ $n\ge2$are real and $(n-1)\ a_1^2 -2n\ a_2 <0$ prove that at least two roots of the equation $x^n+\ a_1x^{n-1}+\ a_2x^{n-2}+...+\ a_n=0$ are imaginary. Manually i am able to prove it as $\ a_2$ is always positive.…

roots

asked Aug 04 '18 at 02:08

Samar Imam Zaidi

8,800

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2 answers

Integer Difference Between Roots

Are there two numbers, x and y, such that neither is a perfect square, and the difference of their roots is an integer? Can you find x and y such that the difference gets arbitrarily close? What about other powers?

roots

asked Jul 23 '18 at 14:21

William Grannis

1,844

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2 answers

How to take "a" as positive and "b" as negative root of quadratic equation in this question?

Hi, I am not getting how to take "a" as negative root and "b" as positive root, while I am only having X in my quadratic equation. What is the connection of a and b with this quadratic equation in this question? My approach to this question: I…

roots

asked May 14 '18 at 10:01

Sumaira Rounaq

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2 answers

Exponential equation with three summands

I had a simple looking math problem the other day: Solve for $y(x) = 0$: $$ 10^{2x} - 101 \cdot 10^x + 100 = 0$$ Since I have three summands, I cannot just put them to either side of the equation and apply $\log_{10}$ to it. And I cannot see how…

roots

asked Jan 05 '13 at 12:27

Martin Ueding

4,523

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1 answer

Equation with absolute values (another)

How many roots (finite number) can equation have? $$ \sum\limits_{i = 1}^{40}|a_i - x| = \sum\limits_{i = 1}^{40}|b_i - x|.$$ I think there is at most one, but I don't know how to prove it. Any ideas?

roots

asked Mar 18 '18 at 15:07

Konstant

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4 answers

If $ax^2+bx+c=0$ has $2$ roots, one root is twice the other, find expression for $b$

$ax^2+bx+c=0$, has two roots with one being twice the other, so $x$ and $2x$ I need to find an expression for $b$ (in terms of $a$ and $c$) I know $b = \dfrac{-ax^2-c}x$, but I don't know how to use the roots and how it would affect the answer

roots

asked Feb 22 '18 at 07:39

C.Cam

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3 answers

A difficult function question, seems unsolvable

Let $f(x)$ be a function which satisfies $f(2014+x)=f(2014-x)$ for all values of $x$. If the graph of $y=f(x)$ has exactly 3 real rots, find the sum of these roots. I have no idea how to begin. Any help?

roots

asked Jan 31 '18 at 15:02

QuIcKmAtHs

1,451

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3 answers

Roots of nonlinear equation

Can anybody help me finding a good way to (approximately) figure out the first, lets say $200$, positive roots of $$\tan(x) + 2 \ell x - \ell ^2 x^2 \tan(x) = 0,$$ where $\ell$ is just a constant? I believe there will be no analytic expression, so…

roots

asked Jan 10 '18 at 17:56

Konstantin

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1 answer

Rolle's theorem with a supplementary condition

I have to find the types of roots (i.e real or complex) of the equation $$ 11^x + 13^x+ 17^x -19^x = 0 \dots (1) $$ If $$ f(x) = 11^x + 13^x+ 17^x -19^x = 0 $$ , then obviously $ f'(x)= 0 $ has a 0 solution, and indeed every derivative of $f(x)$ has…

roots

asked Sep 02 '17 at 16:32

hiren_garai

1,193

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1 answer

Different way of finding square roots of numbers?

this is my first post here and I wanted to run something by people who are more knowledgeable than I. In the past couple days I've decided that I need to teach myself more advanced mathematics as it is of great importance to my studies in physics,…

roots

asked Aug 25 '17 at 19:16

Craiger1987

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4 answers

Root of the equation $x^2+ix+2=0$

What are the roots of the equation $x^2+ix+2=0$, where $i=\sqrt{-1}$? $(-1, 1)$ $(-2i, i)$ $( i, 1)$ no root exists I don't know the method for finding roots of this type of equation. I have tried by the method of $b^2-4ac$ but it doesn't work

roots

asked May 17 '17 at 09:42

rujul mankad

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