The sum of non real roots of the polynomial equation $x^3+3x^2+3x+3=0$
What is the sum of non-real roots of the polynomial equation?
Get image pixels of prescribed color Are we inside a black hole? When/Why Did Love Escape Voldemort? We know that Voldemort does not love. He does not understand it, nor (generally) the magic that it possesses. He knows  of the sort.  [...] &quot;you possess in such quantities and which Voldemort has not at all.&quot; [...] &quot;because he could not bear to reside in a body so full of the force he detests. In the end, it mattered not that you could not close your mind. It was your heart that saved you.&quot; (Harry Potter and the Order of the Phoenix, page 1075)  The above confirms it (although I believe there is a better quote), though  reinforces it. The fact that he hugs so awkwardly shows that he does not really know how, due to his lack of love. I realize that Voldemort's appearance started to change after he started to create Horcruxes, but surely he had an ounce of love when he was a child? The hugging scene perhaps shows that he never once loved his whole life (possibly due to the love potion with his parents?). If so, when did Voldemort begin to have no love at all, and why? setting up subdomain on ubuntu server Several companies are commercializing tests for telomere length such as this one . I understand the basic mechanism for why telomeres shorten during DNA replication, but how good is the evidence that telomere length is a reliable indicator of healthspan/lifespan? Canonical Question  I want to do &lt;some really cool thing&gt; with a lightning:datatable, but I can't seem to figure out how to do it. I checked the , but I did not see a way to implement &lt;this really cool feature I need&gt;.  Perhaps I want to provide tooltips, or a pick list, or alter the behavior of the menus, or display images, or show a custom component I created, or define a new row-level click behavior, or alter the keyboard event handlers, etc.  Can I somehow do this? Show that there's no continuous function that takes each of its values $f(x)$ exactly twice. I need to prove the following:  There's no continuous function $f:[a,b]\to \mathbb{R}$ that takes each of its values $f(x)$, $x\in [a,b]$  exactly twice.  First of all, I didn't understand the question. For example $x^2$ takes $1$ twice, in the interval $[-1,1]$. Is it saying that it does not occur for all $x$ in the interval? But what about $f(x) = c$? Is it saying that it does not occur only exactly $2$ times, then? I have no idea about how to prove it. I know that for $f(x)$ such that $f(a)&lt;f(x)&lt;f(b)$, if $f$ is continuous then there is a $c\in [a,b]$ such that $f(c) = f(x)$.  Now, there's the following proof in my book and I really wanted to understand it, instead of just getting a new proof  Since the interval $[a,b]$ has only $2$ extreme points, then the maximum or minimum of $f$ must be in a point $c\in int([a,b])$ and and in another point $d\in [a,b]$. Then, there exists $\delta&gt;0$ such that in the intervals $[c-\delta, c), (c,c+\delta)$ (and if $d$ is not extreme of $[a,b]$, $[d-\delta, d]$) the function takes values that are less than $f(c) = f(d)$. Let $A$ be the greatest of the numbers $f(c-\delta), f(c+\delta), f(d-\delta)$. By the intermediate value theorem, there are $x\in [c-\delta, c), y\in (c, c+\delta]$ and $z\in [d-\delta, d)$ such that $f(x)=f(y)=f(z)=A$. Contradiction.   Well, why the last part? Why is it that I can apply the intermediate value theorem to these values? For example, $&lt;f(c-\delta)&lt;p&lt;f(c)$, then by the theorem I know that there exists $m\in [c-\delta, c)$ such that $f(m) = p$. Same for the other intervals. But what guarantees thhat the greatest of the values between  $x\in [c-\delta, c), y\in (c, c+\delta]$ will be inside the intervals $[c-\delta), c), (c,c+\delta), [d-\delta, d)$? Is it possible to mark the same tag as "Interesting" and "Ignored"? Can you mark the same tag as both interesting and ignored? If you can, what is the resulting appearance of a question with that tag? Every time I touch an object a full-render starts I don't know what setting I switched, or what happened, but for some reason now every time I move, scale or rotate an object in the 3d View - blender starts a render. I am not talking about the 3d View being in "Rendered" mode. I am talking about the same behavior as when you click the "Render" button (switch to image editor, begin full render). This is driving me crazy and I can't seem to figure out how to turn it off or what I did to start it. It happens whether I use the mouse or keys. If I open a new document the behavior goes away so it is probably a preference setting(?) If you can help, I will be eternally grateful.  Thanks in advance. I know there is a ton of questions and answers about this topic, but none answers my question sufficiently.  Let's say I have a viewport view that I want to render in Cycles. Pressing ALT CTRL Numpad 0 aligns the camera to this view, but it does not solve the whole problem. The thing is, I want PRECISELY this view on the render, preferably in one click, without manually moving the camera back-and-forth, changing sensor sizes etc. fiddling that will remove the unwanted border that appears and blocks the viewport partially. This whole activity wastes a lot of precious time especially if you do this 10 times a day.  What this dream action should do:   match the render resolution (proportions) to the resolution of the current view (can the resolution of current view be read by a Python script?) make the entire view the camera view, without any borders, passe-partout etc. by automatically maneuvering sensor sizes etc. whatever is necessary to make it exactly the same view, the same camera lens angle.   Is it possible to write such a script that would do it all in one click? I don't want to watch the prisoner cart ride to the execution: is it possible to skip this?   If so, how? Can I replace the intro movie file by some empty video? How to blur a texture node in cycles material? For a Cycles material I need to blur a texture. If the texture where a Texture Image node, I can blur the image before adding it but in my case I need to blur a Voronoi Texture and so I can't do it.  I have searched but I didn't find a blur node. Can this be achieved? Investment options for f1 visa students in USA I am foreign graduate student in USA. I recently completed my undergrad (from USA) and have a bit of money saved up. I know that F1 students cannot work off campus and other business activities such stock trading etc are prohibited as well. I wanted to know if opening an account in an investment management firm like Charles Schwabb or Betterment is allowed. I would not be working but I will still be earning a small interest on my deposits. If that is not allowed, are there any good and legal ways for foreign students to earn a little interest on savings? Overcoming ~5000 File Document Library Limits Microsoft technet states that document libraries have a file limit of 30 million items:    In practice, numerous features seem to break once there are more than 5000 items in a Document library - not just in the initial directory listing - but as a recursive total. For example, you may be able to list folders, but setting permissions or deleting files is met with errors.  Are there any configuration options or optimizations that can be used to relax these limits?  A workaround would be to split folders into separate document libraries, but in our case, with over 5 million files, this would result in a minimum of 1000, 5000 file document libraries and likely many more. At that point we're likely shifting the problem into the library view.    A major showstopper is the effect this has on Sharing - a user trying to share a folder with more than 5000 aggregate items simply fails. I'm investigating the effect (if any) the resource throttling suggestion below has on this. I get different lightning render with the same scene camera setup.  Cycles render (both experimental and supported feature set) gets weaker lightning and needs more energy.  How can I get the same lightning and reflection setup with EEVEE and Cycles? It is a win7 ultimate x64 machine. The machine was in a domain where it got those group policy settings. Now it has left the domain but it still receives the settings from the group policy. For example, the power options. I set a certain power option but soon it will be reset to another power option which is endorsed by the domain.  Is there a way to remove the settings? Paucity of words for relationships bash function cannot change the value of a local variable when called by $() The following code works differently depending on which way Parse_Short_Switches() is called.  After calling the function 'Parse_Short_Switches' by using result=$(Parse_Short_Switches), the value of $error_flag is NOT set to -1 as I would expect.  After calling the function 'Parse_Short_Switches' by simply using Parse_Short_Switches, the the value of $error_flag is set to -1 as I would expect.  Any help would be greatly appreciated.  Thanks  #!/bin/bash  function Parse_Short_Switches() { echo "error_flag inside of the function= $error_flag" 1&gt;&amp;2 error_flag="-1" echo "blah blah ..." }  # --- MAIN --- error_flag="999" echo "error_flag= $error_flag" #result=$(Parse_Short_Switches) Parse_Short_Switches echo "error_flag= $error_flag" Installing Guest Additions causing problems theorem numbering: section counter but remove the section number