find the answer in terms of $a$ and $b$ only ($a, b$ are roots of $\ x^4 + x^3 - 1 = 0$
If $a$ and $b$ are two roots of $x^4 + x^3 - 1 = 0$ prove that $ab$ is a root of $x^6 + x^4 + x^3 - x^2 - 1$.
Why should I avoid multiple inheritance in C++? Is it a good concept to use multiple inheritance or can I do other things instead? Script for display wrapper class Account list of records? Hi i am trying to write script for display list of records from wrapper class.   @remoteaction     public static wrappercls getaccounts(){         string account = 'select id,name,accountnumber from account';         listacc = database.query(account);         count = listacc.size();         system.debug('#####'+count);         wrappercls wra = new wrappercls(count,listacc);         return wra;     }      public class wrappercls{         public integer count11;         public list&lt;account&gt; account;          public wrappercls(integer count11,list&lt;account&gt; account){             this.count11 = count11;             this.account = account;         }     }    This class returns list of account records and record count parameter.Need to display these records in page.Is it possible if possible Please help me on this..  Script  &lt;script&gt;   function getallaccounts(){     exremote.getaccounts(         function(result,event){             if(event.status){              }             else {              }        },{escape:true}     ); } &lt;/script&gt;   Thanks in Advance... When handling multiple white-on-transparent png images, I am hindered by the fact that the thumbnails of these images are all-white. Both Adobe Bridge CS6 and Windows Explorer suffer the same problem, I can't discern between two of these pngs.  Is there a way to make these thumbnails useful? Is there some setting I missed that allows changing the thumbnail background colour for a png -- now a deafult white? Using nohup to keep a script running indefinitely I am very new to Linux and I've only been using it to SSH to my web server using Putty. The issue I am having is this:  Basically I've got 2 php scripts. One get_tweets.php constantly listens for tweets on twitters Streaming API whilst the other - parse_tweets.php logs these into a db. In order for these to work they've to be kept running continuously.   I've been using the following commands to run them in the background and from what I've seen they run for most of the day, however whenever I log on to my computer in the morning the scripts have stopped and I've to run commands again.  nohup php my_script.php &gt; /dev/null &amp;   I'm just wondering if that is normal based on the commands I am using, should they run indefinitely when using nohup and if not what is the alternative? A CRON job?  Thanks for the help How to start a GUI software on a remote Linux PC via SSH Sometimes I need to start XMBC media player or other GUI software a one of my PC (small Xubuntu PC used as a media center).  Usually I do this starting a X11vnc server on the remote PC via SSH and than connecting with an Xvnc client to the Xfce desktop.  Is there a way to start a GUI software on a remote Linux PC via SSH?  Thanks! Recommendations for good Newtonian mechanics and kinematics books What are some good books for learning the concepts of Kinematics, Newton laws, 2D Motion of Object etc.? When learning a new subject, I would frequently use lecture notes found somewhere in the Internet. When writing a paper (or a master thesis, as in my case, but the rules should be similar, I believe) one should give some reference for used results which are not common knowledge, if I understand correctly. This make me wonder: what do I do if I want to reference a result I found in some notes?  The natural thing to do would be to just add these notes to bibliography. What format would be preferable for this? Note that there will generally not be much publishing information, perhaps not even a definite year and place. (A BibTeX template would be .)  Secondly, is it OK to cite such materials as a reference? I've noticed this a few times on the Feed activity on the Android app, but never thought anything of it.  Why does this question (How To auto enable checkbox?) appear as "Unanswered" when there is an icon which denotes there are 5 answers, one of which has been marked as the answer?  Dragging down to refresh doesn't seem to clear the unanswered flag either.  Device: Nexus 5 Edit answer draft is broken The Edit Answer Draft button is broken.    Press Back with text in an answer box. The Edit answer draft bar does not appear.     Seems like an onBackPressed() issue.  Also:   Press ← with text in the answer box The bar appears. Click the bar The answer box is blank.   Seems like the answer isn't properly carried between the Fragments.  Either way, you lost everything you wrote.  Can somebody test this? And especially without a confirm dialog, it is a brush of the finger to lose a long post of code or something.   I hope this report will help because I like the app (I'd say 4/5 stars) but the bugs are preventing a solid 5 stars.   Stack Exchange 1.0.73 Samsung Galaxy S II Skyrocket I727 Android 4.1.2 Storing Images in DB - Yea or Nay? I drew a parallelepiped that is spanned by three vectors, and we know the volume is given by the absolute value of the determinant of the matrix - with the three vectors arranged in rows (or columns, since $detA = detA^T$).  How can I draw the tetrahedron from this parallelepiped to convince myself it is indeed 1/6th of the volume, i.e., 1/6 * |detA|?  Thanks, It's clear to me by inspection that if we fix $\beta = \frac{1-\mu}{\mu} \alpha$ (thereby fixing the mean) and let $\alpha \rightarrow 0$, the Beta distribution approaches a Bernoulli($\mu$) distribution.  For example:  par(mfrow = c(1, 2),     oma = c(0, 0, 1.5, 0)) xx = seq(0, 1, length.out = 1000) mus = c(.2, .7) for (ii in 1:2) {   mu = mus[ii]   matplot(xx, sapply(10^(-1:-5), function(al)      pbeta(xx, al, (1-mu)/mu * al)),     type = 'l', lty = ii,     main = paste('Mean:', mu),     ylab = 'Cumulative Probability', xlab = 'x') } title('Beta Approaches Bernoulli', outer = TRUE)     That is, if $X \sim B(\alpha, \frac{1-\mu}{\mu} \alpha)$, its CDF $F_X(x; \alpha, \mu)$, satisfies  $$ \lim_{\alpha \rightarrow 0} F_X(x; \alpha, \mu) = 1 - \mu = F_Y(x) \quad \forall x \in (0, 1)$$  Where $Y \sim$ Bernoulli($\mu$), and the convergence is non-uniform. I tried to do a more formal proof of this but couldn't make any progress, even in simple cases (like $\mu = \frac12$). The  makes reference to the $\mu = \frac12$ case several times without proof. Perhaps I'm missing something easy about doing the integral, or some fact about the Beta/incomplete Beta function. Any help would be appreciated! Let's say you have the ability to shine some light into a perfectly round sphere and the sphere's interior surface was perfectly smooth and reflective and there was no way for the light to escape.  If you could observe the inside of the sphere, what would you observe? A glow? And would temperature affect the outcome?  Seems silly, it's just something I've always thought about but never spent enough time (until now) to actually find an answer. Is there a good Valgrind substitute for Windows? What happens if my flight out of the Schengen area is cancelled on the last day of my visa? Most people know the famous equation:    What were his steps of thinking for this equation that helped us discover so much about our world? Change the default editor when sudo visudo When doing sudo visudo, the default editor is nano. I want to change it to vi or vim.     I already made vim the default editor, and use it as a substitute for gedit to open php, .txt, .c and .h files, by placing a vim.desktop file in ~/.local/share/applications/ and by correctly editing either  ~/.local/share/applications/mimeapps.list or /etc/gnome/defaults.list. However apparently this does not apply to nano.    Any clue ? Why does this steam engine fail to run? Does separability imply the Lindelöf property? Does separability imply a sort of Lindelöf property?  Since I can't prove this fact I'm beginning to think that my conjecture is false.  Intuitively, $\mathbb{R}$ has a countable subset $\mathbb{Q}$ which is used to form a countable basis for $\mathbb{R}$ with the usual topology and prove the Lindeöf property. How to convert string to boolean php