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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If $\sqrt{2x-5} + \sqrt{2x} = 7$, find $\sqrt{2x-5} - \sqrt{2x}$

I tried a few things but could not provide myself with a satisfying answer. Pointing me towards the solution rather than giving the answer or solution right up is as welcome. Answer should be: $$- \frac{5}{7}$$
SarpSTA
  • 467
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1 answer

Method of finding roots of this equation

I'm trying to find the roots $\omega_n$ of, \begin{equation} \tan(\omega) = \frac{2b\omega}{b^2\omega^2 -1} \end{equation} I know it must be done numerically, so I would use the bisection method. In order to use that I must know the interval to…
Josh Albert
  • 191
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2 answers

Factoring a polynomial over $\mathbb{C}$

Every polynomial with complex coefficients can be written as the product of linear factors. What are the linear factors of $P(z)=1+z+⋯+z^7+z^8$?
user412211
  • 1
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4 answers

How many real roots does $x^7+14x^5+16x^3+30x-560=0$ have?

How many real roots does $x^7+14x^5+16x^3+30x-560=0$ have? (a) 1 (b) 3 (c) 5 (d) 7 I don't know what approach to use in order to solve this equation. All I know is that the highest degree of this equation is odd hence it is obvious that…
oshhh
  • 2,632
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1 answer

root of bijective function

If I know that a polynomial function f(x) mapping (a, b) to (c, d) is bijective(one-one and onto), what is the fastest algorithm(On a single processor RAM machine) to find the root( f(x) = 0 ) of that function?
Soham
  • 11
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Doubt on Descartes rule

If $f(x)=x^7-3x^4+2x^3-k=0$, $k>0$ So putting x=-x in the equation, I am getting two sign changes. However, the problem in my book says three. Also, will the answer depend on the little condition given, ($k>0$)?
Zlatan
  • 651
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finding the values of m, using roots

Consider the equation $4x^2 − mx − m = 0 $ (with unknown x). Find the values of m such that the equation has (a) one (double) root; (b) two distinct (real) roots; (c) no real roots. My working out $4x^2 − mx − m = 0 $ Apply the quadratic formula…
Maggie
  • 41
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1 answer

Help on solving roots given sum of zeros, product of zeros, sum of coefficients are equal.

The sum of zeros, the product of zeros, and the sum of the coefficients of the function f(x) = ax^2 +bx +c are equal. Show that all three of these quantities must equal a. Pls help for school assignment.
1pokepie
  • 11
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2 answers

Finding a value based on the roots of an equation

So I saw this question recently: Known $a^2+b^2+6a-12b+45=0$. Find $\dfrac{b-a}{b+a}$. I tried to factorize it but I don't really know how. Can someone help me with this?
blastzit
  • 800
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1 answer

Roots of a fourth order polynomial

I am looking for the roots of $x^4=-1$, I have written $ -1 $ using Euler as $e^{j180}$. Therefore, $x=\pm e^{j45}$. But the fourth order equation should have two other roots, how can I get them?
Jack
  • 145
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1 answer

Integer values of a rational function

How does one analytically determine the integer values of a rational function $f(x)$$=$$\frac{40-8x}{8x+2}mod1$ where $x$ is an element of the rationals? I just gave the function listed as an example, I would like to know the generally preferred…
user3108815
  • 301
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4 answers

How do I form this equation?

If $A$ and $B$ are the root of the equation $3x^2-4x-9=0$, what is the equation whose roots are $(A+3)/(A-3)$ and $(B+3)/(B-3)$
HackToHell
  • 269
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2 answers

Roots (Algebra)

This question consists of multiple questions but I am stuck on the very last one but without showing the first two the last one will be hard to understand so I'll show all my work: 13a) $w$ is one of the complex cube roots of $1$ $Show$ $that$ $$…
bigfocalchord
  • 5,597
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1 answer

Newton's sums on a polynomial

Let $S$ denote the sum of the $2011th$ powers of the roots of the polynomial $(x − 2^0)(x − 2^1)\cdots(x − 2^{2010}) − 1$. How many $1$’s are in the binary expansion of $S$? Progress: I used Newton's sums in order to find that $a_nS_1 + a_{n−1} =…
user19405892
  • 15,592
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3 answers

Show that there exists a root of the equation

Show that there exists a root of the equation $ x^2-x-1= \frac{1}{x+1} $ I don't know where to start. I need hints.
Lyndt
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