6th degree equation The number of real roots of  $$ \frac{3}{x-3}+\frac{5}{x-5}+\frac{17}{x-17}+\frac{19}{x-19} = x^2 -11x -4 $$ How to solve without actually finding the roots or is it the only way? I know that if the equation changes it's sign between two no.s it will have at least one root contained in them.
Let $m$ be the largest real root of the equation $\frac3{x-3} + \frac5{x-5}+\frac{17}{x-17}+\frac{19}{x-19} =x^2 - 11x -4$ find $m$ Let $m$ be the largest real root of the equation $$\frac3{x-3} + \frac5{x-5}+\frac{17}{x-17}+\frac{19}{x-19} =x^2 - 11x -4.$$ Find $m$.   do we literally add all the fractions or do we do something else  I have no clue how to solve this
Understanding the "Birthday Problem" How to call the method correctly in Preference.OnPreferenceChangeListener() While googling, I see that using  can be slow.  has a  method that is available as well.  Is there an efficient way in java to get the file size? 'Thank you for taking your time writing' or 'Thank you for taking your time to write' ? A person gave me an answer on English.SE and I commented:     Thank you for taking your time writing this wonderful answer!   Now, looking at the sentence in retrospect, even though I am not a native English speaker (duh, otherwise I wouldn't be asking a question on ELL.SE), I find the sentence a bit odd.  To get my point across, let me rephrase the sentence:     Thank you for taking your time to write this wonderful answer!   With my relatively little knowledge and understanding of English, I feel that using 'writing' (as I did in the original sentence) emphasizes the very process of writing the answer, whereas using 'to write' emphasizes the mere fact that an answer has been given, and a wonderful one at that.  This is exactly why I feel the original sentence is a little bit awkward and the second, revised one would have been more apt.  Am I correct or are the quoted sentences virtually synonymous? Tentative definitions in C and linking If $AB = I$ then $BA = I$ What do you call someone who pretends to be your friend but is actually your enemy?  A friend suggested spy for me, but that does not nearly describe the word I need for an English project. The character is very good at manipulating how people see him. He's a good liar. And pretends to be your friend but actually is your enemy. Prove that $\binom{m+n}{m}=\sum\limits_{i=0}^m \binom{m}{i}\binom{n}{i}$ How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data? Let's say we have the statistics given below  gender mean sd n f 1.666667 0.5773503 3 m 4.500000 0.5773503 4   How do you perform a two-sample t-test (to see if there is a significant difference between the means of men and women in some variable) using statistics like this rather than actual data?  I couldn't find anywhere on the internet how to do this. Most of the tutorials and even the manual deal with the test with the actual data set only. Let $p$ be a prime number . The order of a $p$-Sylow subgroup of the group $GL_{50}(F_p)$ of invertible $50\times50$ matrices with entries from the finite field $F_p$,equals which of the following    1.$p^{50}$ 2.$p^{125}$ 3.$p^{1250}$ 4.$p^{1225}$    I think order of this  group is $p^{2500}$  .A  sylow p-subgroup of order $P^k$ divides  order of the group but $p^{k+1}$  does not. I confused here how to apply these things . Dual VGA Cards Intel/ Nvidia This is my first post in this forum. I am new to Linux, just installed Ubuntu 11.10 on my Sony Vaio VGN-Z12 with two graphic cards Intel and NVidia Geforce 9300 GS.  After the installation the lightdm works on Intel card but with very law display quality. I installed Nvidia driver from the official website as well as this PPA.  sudo apt-add-repository ppa:ubuntu-x-swat/x-updates sudo apt-get update sudo apt-get install nvidia-current       Once I installed the driver and run nvidia-xconfig which creates xorg.conf file, the xserver will not start with error "no screen". If I delete the xorg.conf file then I am able to start the xserver normally but with intel display (bad quality) Find all solutions to $x^9 \equiv 25 \pmod {29}$ Question on the correlation between two dependent variables I'm working on this question and it's stumping me.     Let $S_n = X_1 + \ldots + X_n$ (with $n&gt;=1$) be a random walk with $X_1, \ldots, X_n$ be iid RV's.   $$ E(X_k)=\mu,\,{\rm Var}(X_k)=\sigma^2.  $$   Find the covariance of $S_n$ and $S_m$   Can anyone help out? I am trying to use the equation: $${\rm Cov}[S_n, S_m] = E[S_nS_m] - E[S_n]E[S_m]$$  but can't quite figure it out. Using SQL Server, how do I split a string so I can access item x?  Take a string "Hello John Smith". How can I split the string by space and access the item at index 1 which should return "John"? Basically, I'm trying to override some files of the Uncode theme. But this is not a theme-specific question: it can be applied to any theme. The Uncode theme has a custom dir 'partials' (/uncode/partials/) that contains some layout elements. On my child theme I created a 'partials' folder as well (my-child-theme/partials), but the inner files seem not to be overridden. Is it normal? WP docs say that any file of the same name should be overridable, but is seems that's not true. Am I doing something wrong? How do I get an array of repeated characters from a string using LINQ? Second-order non-linear ODE $2tx'-x=lnx'$  I differentiated both sides with respect to x:  $x'+2tx''=\frac {x''}{x'}$  Substituting $p=x'$,  $p+2tp'=\frac{p'}{p}$  But I have no clue what can I do from here on.  EDIT: $t$ is the non-dependent variable. How to quit Skype on Android? Unexpected AdjacencyMatrix output Should words be capitalized for being religious terms? While googling about whether "atheist" should be capitalized, and skimming past posts by people blogging about atheism rather than about English grammar, I came across    It says     [Capitalize] Religions and religious terms       Examples:      Catholicism, Hinduism, Buddha, the Bible, Christian, the Ten   Commandments, Baptist church, Mt. Zion Methodist Church      NOTE: Do not capitalize the following:       Examples:      church, communion, atheist, agnostic, spirituality   but I don't recall hearing of such a prescription before. Wouldn't most of the examples listed be capitalized because they're proper nouns? Are there good examples of words being capitalized solely because they're religious terms?  I'm mainly interested in modern English, rather than days of past where a lot more words were capitalized than they are nowadays.  Somewhat related:  - use "God" when referring to the name of the god of Judaism and Christianity (a proper noun), but "god" when referring to the general concept of a deity (common noun).