Prove that the equation: $c_0+c_1x+\ldots+c_nx^n=0$ has a real solution between 0 and 1.
Prove existence of a real root.
My 2nd great-grandmother, Margaret Elizabeth Armegust or Arbingast, was born 22 Sept 1837 in Ohio and died 24 July 1929 at the Richmond State Hospital, Wayne, Indiana, United States.  She lived for a time in Sparta, Noble, Indiana and Stock, Harrison, Ohio. She was married to John B. Miller on 22 Oct 1859 in Noble and they had at least five children: James, Samuel, Elias, Julia, and John.  I am searching for records from the State Hospital to learn of her diagnosis and treatment. Let $A$ be a square matrix of order $n$ such that $A^2 = I$.  Prove that if $1$ is the only eigenvalue of $A$, then $A = I$. Prove that $A$ is diagonalizable.   For  (1), I know that there are two eigenvalues which are $1$ and $-1$, how do I go about proving what the question asks me? A hidden process, what it is? [root@datacenteronline ~]# ssh root@192.168.1.172 Last login: Wed Apr 17 09:55:45 2013 from 192.168.1.187 [root@localhost ~]# ls /proc/ | grep 2266 [root@localhost ~]# cd /proc/2266 [root@localhost 2266]# ls attr             cpuset   limits      net            root       statm autogroup        cwd      loginuid    numa_maps      sched      status auxv             environ  maps        oom_adj        schedstat  syscall cgroup           exe      mem         oom_score      sessionid  task clear_refs       fd       mountinfo   oom_score_adj  smaps      wchan cmdline          fdinfo   mounts      pagemap        stack coredump_filter  io       mountstats  personality    stat [root@localhost 2266]# ls -al /proc/2266 total 0 dr-xr-xr-x   7 apache apache 0 Apr 17 09:45 . dr-xr-xr-x 266 root   root   0 Apr 17 09:11 .. dr-xr-xr-x   2 apache apache 0 Apr 17 09:45 attr -rw-r--r--   1 root   root   0 Apr 17 09:45 autogroup -r--------   1 root   root   0 Apr 17 09:45 auxv -r--r--r--   1 root   root   0 Apr 17 09:45 cgroup --w-------   1 root   root   0 Apr 17 09:45 clear_refs -r--r--r--   1 root   root   0 Apr 17 09:45 cmdline -rw-r--r--   1 root   root   0 Apr 17 09:45 coredump_filter -r--r--r--   1 root   root   0 Apr 17 09:45 cpuset lrwxrwxrwx   1 root   root   0 Apr 17 09:45 cwd -&gt; / -r--------   1 root   root   0 Apr 17 09:45 environ lrwxrwxrwx   1 root   root   0 Apr 17 09:45 exe -&gt; /usr/local/apache2/bin/httpd dr-x------   2 root   root   0 Apr 17 09:45 fd dr-x------   2 root   root   0 Apr 17 09:45 fdinfo -r--------   1 root   root   0 Apr 17 09:45 io -rw-------   1 root   root   0 Apr 17 09:45 limits -rw-r--r--   1 root   root   0 Apr 17 09:45 loginuid -r--r--r--   1 root   root   0 Apr 17 09:45 maps -rw-------   1 root   root   0 Apr 17 09:45 mem -r--r--r--   1 root   root   0 Apr 17 09:45 mountinfo -r--r--r--   1 root   root   0 Apr 17 09:45 mounts -r--------   1 root   root   0 Apr 17 09:45 mountstats dr-xr-xr-x   6 apache apache 0 Apr 17 09:45 net -r--r--r--   1 root   root   0 Apr 17 09:45 numa_maps -rw-r--r--   1 root   root   0 Apr 17 09:45 oom_adj -r--r--r--   1 root   root   0 Apr 17 09:45 oom_score -rw-r--r--   1 root   root   0 Apr 17 09:45 oom_score_adj -r--r--r--   1 root   root   0 Apr 17 09:45 pagemap -r--r--r--   1 root   root   0 Apr 17 09:45 personality lrwxrwxrwx   1 root   root   0 Apr 17 09:45 root -&gt; / -rw-r--r--   1 root   root   0 Apr 17 09:45 sched -r--r--r--   1 root   root   0 Apr 17 09:45 schedstat -r--r--r--   1 root   root   0 Apr 17 09:45 sessionid -r--r--r--   1 root   root   0 Apr 17 09:45 smaps -r--r--r--   1 root   root   0 Apr 17 09:45 stack -r--r--r--   1 root   root   0 Apr 17 09:45 stat -r--r--r--   1 root   root   0 Apr 17 09:45 statm -r--r--r--   1 root   root   0 Apr 17 09:45 status -r--r--r--   1 root   root   0 Apr 17 09:45 syscall dr-xr-xr-x  29 apache apache 0 Apr 17 09:45 task -r--r--r--   1 root   root   0 Apr 17 09:45 wchan   Cound anyone tell me what it is? Is a sentence always grammatically incorrect if it has no verb? Is the following grammatically correct? My friend says the second sentence is grammatically incorrect, but couldn't explain why.     I have always been fascinated by statistics. The different ways in   which you could look at data and infer knowledge from it. Why must local variables have initial values? How do I capture artificial light sources better? I am quite new to photography and was looking into how I can take better indoor photographs, particularly around night time.  I'm currently in a hotel room for the night and decided to try and take a picture of my room to test out my tripod which I haven't used before. However I noticed no matter what I set my camera settings to the artificial lights (particularly the lamp on the left, image attached) just appeared very washed out. You can't tell any detail about the lamp shade all you can see is just some sort of light but not much to it.  I tried a variety of fstop/shutter speed settings and tried a variety of ISO settings but they all appeared pretty much the same unless I massively underexposed the image.  Given that I wondered whether the solution would be to take a HDR image or take a normal exposure and an underexposed image and blend them later? I understand that artificial light like this can be very hard and harsh but I wondered if there's a way of improving the result with looking away from it?  I wasn't trying to take any particular special picture here but just test out my camera a bit more but this was the first thing I noticed and I didn't know how to fix it. Any tips would be greatly appreciated. When $f(x+1)-f(x)=f'(x)$, what are the solutions for $f(x)$? Java has a convenient split method:  String str = "The quick brown fox"; String[] results = str.split(" ");   Is there an easy way to do this in C++? See how many duplicates of a post? Can I see how many duplicates there are of a post? I.e. how many posts have been labelled as duplicate because of this post? If so, how? And can I also get a list of these duplicated posts? I have a bash script that makes a cURL request and writes the output to a file called resp.txt.  I need to create an exclusive lock so that I can write to that file and not worry about multiple users running the script and editing the text file at the same time. Here is the code that I expect to lock the file, perform the request, and write to the text file: ( flock -e 200 curl 'someurl' -H 'someHeader' &gt; resp.txt ) 200&gt;/home/user/ITS/resp.txt  Is this the correct way to go about this?  My actual script is a bit longer than this, but it seems to break when I add the flock syntax to the bash script. If someone could explain how these file descriptors work and let me know if I am locking the file correctly that would be awesome! Why do people sometimes use the past perfect form of a verb when the past would suffice? (e.g. "you had mentioned") Is smell a bad way of determining whether meat is still good? Graphics file extensions and their order of inclusion when not specified When using 's \includegraphics you can specify the file extension or not. For generic use and perhaps portability, extensions are commonly dropped. The types of "approved" inclusions and their order of precedence depends on the driver/compiler being used. What are these driver-defaults?  Related: What is the difference between "citizen" and "denizen" Citizen: 1. A legally recognized subject ornational of a state or commonwealth, either native or naturalized. 2. An inhabitant of a particular town or city.  Denizen: 1. An inhabitant or occupant of a particular place.  Same thing? Why does an environment's label have to appear after the caption? \documentclass{article} \usepackage{algorithm}  \begin{document} \setcounter{section}{54} \section{A section with no label} \begin{algorithm} \label{myalg} \caption{An algorithm with the label `myalg'.} \end{algorithm} Reference to myalg: \ref{myalg}. \end{document}   With this code, the reference givens 55 (the section number); if I move the label after the caption command, I get the correct reference (1).  Why should this be the case? I find it confusing: when thinking about an algorithm as an environment, you expect to be able to label it right after you began it. At the very least I would expect some kind of error or "??" to appear, rather than the previous environment or reference-able entity being used. Run MySQLDump without Locking Tables My 13 year old daughter says she wants to be a boy. This is out of character for her. Is this a phase? My daughter, 13, has said she wants to be a boy. A little background: we moved to a new state a year and a half ago. In her new school, she felt isolated among her peers until she met a girl in art, and became good friends. She joined the drama club, and made  friends with some 8th graders. They joined “the diversity club”. This club is a LGBT club. The kids put on a play they wrote and starred in, which had homosexual connotations. “Romeo and Juliet”, but script  rewritten to include  2 females as the couple, for instance.   My daughter got so wrapped up in it, that her life was as if she was copying the play. She’s no longer friends with the friend from art, but remains close with the 8th grade crowd. They all labeled themselves. One week, my daughter said she was gay, then, changed to bi, then onto pan. (I had to google that one). Now she is emphatic about being disgusted with her body and wants to be a boy. She wants to donate all the “girly” clothes she picked out last year, and tossed out all the makeup she bought a few months ago.   All her life, she was the classic girly girl. She had crushes on boys, and she and this boy were inseparable since first grade. She was sad when it came time to move away. When we settled here, she became sullen and angry, putting herself down. She now sees a therapist who she really likes. We’ve been working on her self esteem issues. She’s wanting us to call her “he” and by a male name. I can’t do that. She’s my daughter. She is female. Had we seen this coming, maybe I could come to accepting. But it happened out of the blue.  Sometimes the old her comes back-I got a makeup sample and she was interested in trying it, looked at me, then quickly put it down and said “ewww, makeup”—just a few months ago, she bought a bunch. She’s now wanting to wear boys clothes and talks of wearing a suit to her prom. She is very impressionable, and seems affected by viral YouTube videos about kids coming coming out to their mothers, and the mothers gleefully embrace with happy tears. She has told me when she’s 18, she’s having her breasts removed.    Nothing seems normal to me anymore-in terms of how she always was-this new situation just doesn’t fit.  My gut tells me this is a phase.  I’m hoping it’s a phase. But with all I’m seeing in the media about this, I’m not sure. I love her; this is too much for me to process. I’m a stay at home mom; we were inseparable. I knew her. Until now.:(  She cut off all her beautiful hair, and wears boys shorts, baggy tee shirts, and bought this awful men’s deodorant spray. Please help me sort this out. I’m at my wits end.  Do you think this is a phase? Is this common? How can I update my OpenGL to 3.0 or higher I tried turn on in compizconfig but I does not work. Any solution or it is possible? I would like to draw an arrow like this using TikZ:    This is taken from . I didn't succeed in reproducing the arrow; is somewhat beyond my (extremely limited) TikZ abilities. I don't need all the workflow stuff. I simply want to draw such an arrow at a certain place in my text, e.g. -->  \documentclass{article} \usepackage{&lt;???&gt;} \usepackage{tikz} \usetikzlibrary{&lt;???&gt;} \begin{document} Donec vehicula augue eu neque. Pellentesque habitant morbi \tikz &lt;???code for the arrow???&gt; ; tristique senectus et netus \end{document}   PS: Some explanations in your solution would be much appreciated, otherwise it will be difficult to customize it.