Is solving a quadratic equation using Turing machine impossible?

I’ve just started Algorithms at university. There’s a task to write an algorithm for a Turing machine to solve quadratic equations. The task doesn’t specify if it’s x^2+bx+c or ax^2+bx+c. I’ve searched whole bunch of information over Russian and English Internet.

I did find articles, which say it’s not possible because we’ve got real numbers A, B, C. Please confirm if that’s true. I may not get it correct.. But I think that’s impossible. I still don’t know how to prove my thoughts.

Thanks in advance!

Is longest-path with a specific source and destination impossible in polynomial time?

The problem of finding the longest path in a graph is known to be not be possible in polynomial time, that I am aware of. I am also aware that using DFS or BFS can give the shortest distance between a given origin and destination in a graph. Is it possible to find a longest path from a source vertex to a destination vertex in polynomial time?

Are tiny point-symmetric grids of two Pentominos impossible to solve?

The game of Pentomino is a tiling puzzle game played on a grid. A Pentomino piece is a two dimensional shape of five non-diagonally connected tiles. There are exactly 12 unique pieces (ignoring rotation/reflection). The goal of the game is to fill the board with the available pieces without overlapping.

Pentomino pieces and names

This question concerns point-symmetric boards (not necessarily rectangular) of 10 spaces, i.e. with room for exactly two pieces.

Filling such a board is, of course, trivial when using the same piece twice.

Using the Y-piece twice on a point-symmetric hourglass board: ####  O# OOOO 

However, it seems impossible to do when using two different pieces. Is this true? How could this be proved?

This is not the case for larger boards or larger pieces (more than 5 tiles). Of course, the standard 6×10 board using 12 Pentomino pieces is also a counter example when using more than two pieces. Small counter examples:

Three 5-tile Pentomino pieces (V, P and L pieces) on a 3x5 grid: vvvpp vLppp vLLLL  The 5-tile pieces P, T and F on an oval-shaped point-symmetric grid.  ppTF pppTFFF   TTTF  Two 8-tile pieces on a 4x4 grid: #### #OOO #OOO ##OO 

It feels impossible to play non-D&D RPG’s

I dislike D&D, but it feels like the only choice I have when I want to play an RPG with friends. D&D is so popular and so many people play it exclusively, that it takes way too much effort to even introduce other RPG’s to D&D players, as they generally are too scared to try anything besides it. It feels like D&D is popular sure, but all other RPG’s are still incredibly niche.

How to prevent 2FA (or MFA) being bypassed 100%, impossible to penetrate?

what can I do in order to make 2FA impenetrable, provided that the service has befitting safety measures?

For example, if I have a bank app I can see my bank balance with or I can make purchases or money transfers with, and it has a 2FA having single-usage codes sent to a phone number, would it be safe enough to put a secondary phone unknown to everybody (except the bank of course)?

I mentioned a secondary phone number because obviously potential perpetrator knowing my number could potentially drain out my (hypothetical) bank balance if I put my original phone number as a 2FA step, by using the sim swap technique

And also if there are banks providing a physical code generator, then obviously the problem doesn’t stand in and of itself.

I’d gladly accept any answer mentioning other scenarios or from which I can take additional advices unknown to me.

Is it impossible to Ready a Green-Flame Blade?

I’ve noticed a curious quirk of wording when it comes to the Green-Flame Blade cantrip. Specifically, this tidbit:

As part of the action used to cast this spell, you must make a melee attack with a weapon against one creature within the spell’s range, otherwise the spell fails.

Suppose I want to use my action to Ready a cast of Green-Flame Blade. The thing is, Readying a spell is described as casting it using your action, then holding it until you deliver it with your reaction. I haven’t struck an enemy with a melee attack as part of the casting so… does it fail, and thus prove itself impossible to Ready?

Impossible to run texstudio once installed

I’m running a fresh new installed Ubuntu 18.04.3. So my problem is: when I install texstudio with terminal in the usual way everything seems to run smoothly:

zosiah@zosiah-HP-255-G6-Notebook-PC:~$   sudo apt install texstudio [sudo] password for zosiah:  Reading package lists... Done Building dependency tree        Reading state information... Done The following package was automatically installed and is no longer required:   libqt5concurrent5 Use 'sudo apt autoremove' to remove it. The following additional packages will be installed:   texstudio-l10n Suggested packages:   latex-beamer The following NEW packages will be installed:   texstudio texstudio-l10n 0 upgraded, 2 newly installed, 0 to remove and 0 not upgraded. Need to get 0 B/5.775 kB of archives. After this operation, 16,5 MB of additional disk space will be used. Do you want to continue? [Y/n] y (Reading database ... 365865 files and directories currently installed.) Preparing to unpack .../texstudio_2.12.6+debian-2_amd64.deb ... Unpacking texstudio (2.12.6+debian-2) ... Selecting previously unselected package texstudio-l10n. Preparing to unpack .../texstudio-l10n_2.12.6+debian-2_all.deb ... Unpacking texstudio-l10n (2.12.6+debian-2) ... Setting up texstudio (2.12.6+debian-2) ... Setting up texstudio-l10n (2.12.6+debian-2) ... Processing triggers for desktop-file-utils (0.23-1ubuntu3.18.04.2) ... Processing triggers for man-db (2.8.3-2ubuntu0.1) ... Processing triggers for gnome-menus (3.13.3-11ubuntu1.1) ... Processing triggers for hicolor-icon-theme (0.17-2) ... Processing triggers for mime-support (3.60ubuntu1) ... 

but when I try to run texstudio terminal says:

zosiah@zosiah-HP-255-G6-Notebook-PC:~$   texstudio texstudio: error while loading shared libraries: cannot open shared object file: No such file or directory 

I’ve been googling around for a while but I’ve not arrived to a solution… Any idea? P.S. I’m not being able to install texmaker and emacs25, too. This thing sounds to me pretty strange because until now I’ve never had such problem neither wit synaptic nor with apt and so on… What could be the matter?

Is dispelling nearly impossible to succeed?

The rules for dispelling say:

A Dispelling test is the dispeller’s Counterspelling + Magic [Astral] v. spell’s Force + caster’s Magic (+ amount of Karma spent on quickening the spell, if any) […] Every net hit reduces the number of hits the caster had in casting the spell.

Our mage cast a Force 10 illusion with 8 magic (6 + 2-Force focus). She had 8 hits in her spellcasting test. An enemy mage would like to dispel that illusion.

If I understood the rules correctly, that means the enemy needs at least 19 hits on their dispelling test to even start to affect the spell. The enemy mage has 6 dispelling and 6 magic, so they can’t possibly hope to succeed. On top of that, the attempt will cost them the drain of the 10-Force spell.

Is my understanding of the rules right? Is Dispelling really that weak?