Please help me to answer the following problem:  Let $f(x)=x^3-6x-2\in\mathbb{Q}[x]$ and $L$ be a splitting field of $f(x)$ over $\mathbb{Q}$.   $f$ is irreducible  in $\mathbb{Q}[x]$ and its discriminant is $756$. Up to isomorphism  $\operatorname{Gal}(L/\mathbb{Q})=S_3$     Find an explicit expression of a root of $f(x)$ in term of radicals and use it to write a repeated radical extention $\mathbb{Q}⊂K$ such that $f(x)$ splits in $K$.
Please help me to answer the following problem:  Let $f(x)=x^3-3x-5\in\mathbb{Q}[x]$  Thanks
How to use itemize in Table environment I want to create a table like the picture below, and i wish to itemize the lamba_1 > lamba_2 > 0 using 'item style', which is the cell of each categories. Can someone help me? How do I programmatically log in a user with a POST request? Wall of Sand on Difficult Terrain Looking into  prompted this inquiry:  What happens when you move through a wall of sand on difficult terrain?  This involves the understanding that wall of sand changes the cost of moving 1 foot to 3 feet and that difficult terrain typically changes the cost of moving 1 foot to 2 feet. Function always continuous in a Sobolev Space? Hy everybody got a quick question. I know that all function F in a Sobolev Space has a continuous representative called U such as U=F almost everywhere.  Lets take for example: The Sobolev space on ]-1,1[    the function F(x)=0 on x&lt;0 and F(x)=1 x>0  we can't find a continuous representative because it would be on a larger interval let say ]-eps ,eps[ so not in a Sobolev space the function F(x)=x on x&lt;0 and x>0 and F(0)=1 where we could find the representative U=x   My question is: if F isn't continuous is it sure that it isn't an element of a Sobolev Space? It was given was given as a necessary condition in my course.  Thanks for the help. My primary server with SQL Server 2005 broke down, so I've started up the log-shipped database on the secondary server. The database is live on the secondary server, and I just need to remove the log shipping settings for it, while the primary server is no longer accessible.  It seems that the sp_delete_log_shipping_secondary_database stored procedure should be executed on the secondary server to do this, which "removes a secondary database and removes the local history and remote history", as it is stated on .  Would this also remove the database itself? Or only the log shipping settings for it? And what will it do when the primary server is not accessible?  I must not loose the database on the secondary server, as it is already in use. Is wildcard search possible in Gmail? I have this graphic. I need to change the color of the graphic to hex color: 1485cc...is there a way to make this graphic match that particular hex color hue...without me having to have to re create the graphic. How to correctly install libpng12-0 on the Ubuntu 19.10? For  I need to install libpng12-0 package on the Ubuntu 19.10 system.  I know that it is available .  So I have decided to download this package manually and install it by hand.  On previous Ubuntu versions (such as 18.04 LTS) this trick ends with success, but here on 19.10 it fails in very strange way:   wget http://mirrors.kernel.org/ubuntu/pool/main/libp/libpng/libpng12-0_1.2.54-1ubuntu1.1_amd64.deb sudo apt-get install ./libpng12-0_1.2.54-1ubuntu1.1_amd64.deb  0 upgraded, 1 newly installed, 0 to remove and 0 not upgraded. Need to get 0 B/116 kB of archives. After this operation, 285 kB of additional disk space will be used. Get:1 /home/user/libpng12-0_1.2.54-1ubuntu1.1_amd64.deb libpng12-0 amd64 1.2.54-1ubuntu1.1 [116 kB] Selecting previously unselected package libpng12-0:amd64. (Reading database ... 212864 files and directories currently installed.) Preparing to unpack .../libpng12-0_1.2.54-1ubuntu1.1_amd64.deb ... Unpacking libpng12-0:amd64 (1.2.54-1ubuntu1.1) ...  dpkg: error processing archive /home/user/libpng12-0_1.2.54-1ubuntu1.1_amd64.deb (--unpack):  unable to install new version of '/lib/x86_64-linux-gnu/libpng12.so.0': No such file or directory No apport report written because the error message indicates an issue on the local system                                                                                          Errors were encountered while processing:  /home/user/libpng12-0_1.2.54-1ubuntu1.1_amd64.deb E: Sub-process /usr/bin/dpkg returned an error code (1)   What is wrong here? How can I get libpng12-0 installed on Ubuntu 19.10 system?    Note: the same happens on 19.04, but it is near EOL. How to determine which program is making a certain sound in windows 7? I'm experiencing an annoying "female robotic" sound effect saying "loading complete" at uncertain interval in windows 7.  I want to shut down that noise for good. To do that, I have to determine which program is making this sound. I tried to open the "sound mixer" window, only to find to program last made any sound, one is official GTalk client, one is system sound. I tried to close GTalk and the sound still existed.  I started experiencing this issue not long after I installed a "driver" program for Rapoo E9198 wireless keyboard. Is the Stack Overflow source code available? Geometric intuition behind gradient, divergence and curl LaTeX figures side by side I want to place 2 images side by side in LaTeX. I have 2 .png files and I don't understand how to do it in LaTeX. I have tried many ways but could not get a good result. The descriptions for the editing badges are:     Editor:    Strunk &amp; White:    Copy Editor:    Does "posts" include your own questions/answers, or are these badges just for edits to other people's stuff?  Other questions about how editor badge works:   What if I edit only a question's tags, but not its body? What if I edit both a question's tags and its body? Do edits to Community Wiki posts count? Do edits to answers count? Do edits to tag wiki pages count? Do edits to comments count? (Moderators can edit other users' comments, even outside of the usual five minute window.) Show that $d_2$ defined by $d_2(x,y)=\frac{|x-y|}{1+|x-y|}$ is a metric How do I read image files directly from a zip without extracting to disk? Which fruits and vegetables should be kept in a fridge, and which outside? How to get into Walker in the Wastes as a level 3 Wizard I am building a Wizard character that focuses on using Greater Drought from the Walker in the Wastes prestige class.  The campaign is starting at level 12, so I need to figure out a way to build a Wizard 3/Walker in the Wastes 9.  I am planning on using Southern Magician and Extra Spell to get around the spell requirement, but I'm having trouble qualifying for Heat Endurance by level 3.  We are using a variant rule where, at every level divisible by 3, we get 3 feats instead of 1. At level 3, I'll have 1 feat from level 1, and 3 feats from level 3.  How can I build a character with 11 total levels of Wizard spellcasting and the Greater Drought Walker in the Wastes ability by level 12?  My current character sheet can be found . "As a beginner, I am happy that I learned a new thing."  You will recognize this as your DoReMi-s.( at 4:52)  What is the meaning of the "AS" there and when do we use that?  In depth answers would be appreciated.  Similarly:     Do I have your word as a lawman not to shoot me down like a dog in the street?    Can you explain this sentence?   Can I understand it as a lawman wouldn't shoot down people on the street or wouldn't have his word or what? What is the difference between a[bc]d and a{b,c}d? Why do people use a{b,c}d when there is already a[bc]d? How do I separate hydraulic disc brake pads after pulling the brake while the wheel is off?