Solutions of quadratic equation with complex coefficients, using the quadradic formula.
Quadratic Formula in Complex Variables
Let $f$ be increasing on $[a,b]$ and $a < x_1 < \dotsb < x_n < b$. Show that $\sum_{k = 1}^n [f(x_k^+) - f(x_k^-)]\leq f(b^-) - f(a^+)$. How to tell if a site is using Drupal 7 I know how to check , but is there a way to tell if a site is built with Drupal 7? How to efficiently animate 2D scene spanning sprites in Unity? Our game is a 2D point-and-click adventure game.  One of the levels is set in a factory with conveyor belts that span the scene.  The game is hand animated in 2D and so animating these conveyor belts could potentially take up lots of memory since the sprites are as long as the screen (it's an HD game - 1920 x 1080). I'm not sure if tiled sprite shapes can be animated, so I was wondering if there's a prescribed way to handle larger sprite animation like this - efficiently. X, along with Y, "were" or "was"? I was interested in the following sentence which appeared in a   in The Washington Post, Politics, (WHO RUNS GOV).     She, along with Mark Childress, were set to be Daschle's deputies at   the White House before he stepped down.   Can someone clarify if the fragment "She, along with Mark Childress, were set to" is ungrammatical, as I think it is?  I would reword were with was because I think that the subject of the sentence - obviously, in grammatical terms - is "She", not "She" and "Mark Childress", but I'm not sure on this correction.  More precisely, I'm not so sure that "She, along with Mark Childress" is equivalent to She and Mark Childress with regard to the effects on the grammatical numbers. Does anyone know of a nice (and preferably free) way to integrate Prolog and C#?  Im looking to create a Prolog dll or similar to call from my managed code, and retrieve an answer once all the processing has been complete. Im looking for it to be predominantly one sided (c# calls Prolog).  I have seen  which talks about Prologs real world usage but I was wondering if anyone had either any experience with c# &amp; Prolog? or a nice tutorial/article? Why is $ 561 = 3*11*17 $ the smallest Carmichael number? A composite integer n is a Carmichael number if the only Fermat   witnesses for $n$ are those $a \in \mathbb Z_n^+$ which are not   coprime with $n$. The smallest example of such a number is $561 = 3 ·  11 · 17$   I think I understand the definition, but I don't quite understand why is the smallest Carmichael number is the above mentioned number. Please clarify. Difference between "speed up something" and "speed something up" Both seem to be in common usage, but is there a nuanced difference about when one is more appropriate than the other? Thanks. Ellipsis for overflow text in dropdown boxes Which of these are acceptable? Is one preferable over the other?   "Chemically-deposited tourmaline is never periwinkle." "Chemically deposited tourmaline is never periwinkle."   Also, is the title to the this question asking what I'm trying to ask?  (I realize that there are other questions about hyphenation in similar contexts; I'm asking specifically about -ly adverbs.) Why is foo.hasOwnProperty('__proto__') equal to false? I read on  that the netbook edition of Ubuntu was discontinued and that it is now integrated into the main distribution (as of 11.04).  I tried 11.04 on my new Samsung NC110-A06AU with 10.1" 1024x600 display. Most things worked out of the box, but some (like backlight power control) needed some  before they began to co-operate.  One thing that seems to be an ongoing problem is the resolution.  At 1024x600, most of the dialogue boxes run off the bottom of the screen, including the update manager. I have tried 11.10 beta 1 and it has the same problem.  Is there any way to fix this, or at least make it more usable? (I suspect not). Given the recent rise in popularity of netbooks, do you think Ubuntu will include a low-resolution-friendly version in the near future?  How well does KDE deal with these low resolutions? I noticed KDE Plasma has a netbook interface. Is it worth switching for that? Factoring Quadratics Is there a method to find which numbers to use when simplifying quadratics?   For example $x^2 + 5x + 6$ is easy enough to find, but what if I have bigger numbers, or I have this quadratic expression: $x^2 + 7x – 6$, then it gets very hard to think of a valid simplification.  EDIT: Here's an example: $(x^2 + 5x + 6)/(x + 2)$. When simplifying the first half we get $(x + 2)(x + 3)/(x + 2)$, then we can cancel out $(x + 2)$ and the answer would be $(x + 3)$. The question is: How to always find the right numbers which to put in? (in this example they where 2 and 3) Polygon intersection using turf js pylab.ion() in python 2, matplotlib 1.1.1 and updating of the plot while the program runs Are there any drawbacks to using a wish spell to increase ability scores? If not then what would stop players from just using wish repeatedly and raising their ability scores to 30?  I'm just getting back into RPGs with D&amp;D 5e after not playing for years, and I seem to remember this being covered in the editions we played back then. A generic list of anonymous class In C# 3.0 you can create anonymous class with the following syntax  var o = new { Id = 1, Name = "Foo" };   Is there a way to add these anonymous class to a generic list?  Example:  var o = new { Id = 1, Name = "Foo" }; var o1 = new { Id = 2, Name = "Bar" };  List&lt;var&gt; list = new List&lt;var&gt;(); list.Add(o); list.Add(o1);   Another Example:  List&lt;var&gt; list = new List&lt;var&gt;();  while (....) {     ....     list.Add(new {Id = x, Name = y});     .... } Proving the measure of an increasing sequence of measurable sets is the limit of the measures How do I write to NTFS drives in OS X? I am using cURL to insert data into salesforce. It works with single record but I need to insert multiple records at a time. Is it possible to do so and is it possible via a REST interface? It seems that KNN is a discriminative learning algorithm but I can't seem to find any online sources confirming this.  Is KNN a discriminative learning algorithm?