/sci/ - Science & Math » Thread #12682939

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Anonymous Mon 08 Feb 21:16:22 2021 No.12682939 View Reply Original Report

Quoted By: >>12682966 >>12683047 >>12683062 >>12683394 >>12683405 >>12684302 >>12685664 >>12686758 >>12687240 >>12687963 >>12688675 >>12688681 >>12688899 >>12690669 >>12690880 >>12691516

Can You?

Anonymous

Anonymous Mon 08 Feb 2021 21:22:36 No.12682966 Report

Quoted By: >>12683023 >>12683059 >>12684302 >>12685683

>>12682939
What algebra are we working in here?
If it's the Reals x is -2
If it's the complex numbers, x is any one of -2, 1+i and 1-i
If it's the quaternions, or the bicomplex numbers, or anything else idk

Anonymous

Anonymous Mon 08 Feb 2021 21:34:02 No.12683023 Report

Quoted By: >>12683041 >>12686073

>>12682966
$\mathbb{N}$

Anonymous

Anonymous Mon 08 Feb 2021 21:37:11 No.12683041 Report

Quoted By: >>12683050 >>12686684 >>12689997

>>12683023
No solutions

Anonymous

Anonymous Mon 08 Feb 2021 21:39:05 No.12683047 Report

Quoted By: >>12683070 >>12685683

>>12682939
https://www.wolframalpha.com/input/?i=x%5E3+-+2x+%2B+4+%3D+0

Anonymous

Anonymous Mon 08 Feb 2021 21:39:30 No.12683050 Report

Quoted By:

>>12683041
But anon, the writing by the anime lady says you should be able to solve it.

Anonymous

Anonymous Mon 08 Feb 2021 21:41:19 No.12683059 Report

Quoted By: >>12683291

>>12682966
>What algebra are we working in here?
All the algebra that you can operate, if you know quaternion algebra can you try to solve

Anonymous

Anonymous Mon 08 Feb 2021 21:41:49 No.12683062 Report

Quoted By:

>>12682939
not doing your homework, OP

Anonymous

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Anonymous Mon 08 Feb 2021 21:42:38 No.12683070 Report

Quoted By:

>>12683047
>wolframalpha

Anonymous

Anonymous Mon 08 Feb 2021 22:00:05 No.12683291 Report

Quoted By:

>>12683059
All polynomials over $\mathbb{H}$ have either zero or $\aleph_{k>0}$ solutions, as explored by Ivan Niven. However an analogue of the fundamental theorem of algebra does exist, as each polynomial of degree n with some solutions has all solutions fall into one of exactly n conjugacy classes.

Anonymous

Anonymous Mon 08 Feb 2021 22:22:28 No.12683394 Report

Quoted By: >>12683920 >>12685683

>>12682939
There's an obvious solution, $x=-2$

$x^{3}-2x+4=(x+2)(x^{2}-2x+2)=0$ (Can be found with polynomial division)
$x^{2}-2x+2=0$
$x^{2}-2x=-2$
$x^{2}-2x+1=-1$
$(x-1)^{2}=-1$
$x= 1\pm i$

$x=2$ , $x=1+i$ , $x = 1-i$

Anonymous

Anonymous Mon 08 Feb 2021 22:25:25 No.12683405 Report

Quoted By:

>>12682939
Add and subtract $x^2$

Anonymous

Anonymous Tue 09 Feb 2021 00:54:38 No.12683920 Report

Quoted By: >>12684280

>>12683394
How do you determine what to divide?

Anonymous

Anonymous Tue 09 Feb 2021 02:53:12 No.12684280 Report

Quoted By: >>12685683

>>12683920
$x^{3}-2x+4=(x+2)P$

Solve for the polynomial P

Anonymous

Anonymous Tue 09 Feb 2021 03:00:26 No.12684302 Report

Quoted By: >>12684320

>>12682939
x=2

>>12682966
It's basic PEMDAS jr high shit. Stop being autistic.

Anonymous

Anonymous Tue 09 Feb 2021 03:11:25 No.12684320 Report

Quoted By: >>12688658 >>12688666

>>12684302
You mean -2.
x=2 leads to 8-4+4=8
x=-2 leads to -8+4+4=0

Anonymous

Anonymous Tue 09 Feb 2021 14:08:22 No.12685664 Report

Quoted By:

>>12682939
>child me hates algebra
>adult me loves it
What have I become?

Anonymous

Anonymous Tue 09 Feb 2021 14:12:12 No.12685683 Report

Quoted By: >>12685777 >>12688672

>>12682966
>>12683047
>>12683394
>>12684280
Sure are a lot of brainlet pseuds in this thread.
>Brute force it mate, find a root
>Just use WolframAlpha bro
Pseuds don't know the cubic formula.
>https://math.vanderbilt.edu/schectex/courses/cubic/

Anonymous

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Anonymous Tue 09 Feb 2021 14:25:52 No.12685727 Report

Quoted By: >>12685765 >>12685899 >>12687257

dumb question here but when a polynomial doesn't intersect with the x-axis we use complex roots, what about when a polynomial for example a third degree polynomial intersects with the x axis only once, can i say that it has 1 normal root and two complex ones?

Anonymous

Anonymous Tue 09 Feb 2021 14:41:13 No.12685765 Report

Quoted By:

>>12685727
One real two complex roots

Anonymous

Anonymous Tue 09 Feb 2021 14:46:48 No.12685777 Report

Quoted By: >>12685833

>>12685683
$\displaystyle ax^3+bx^2+cx+d=0 \\ S=2b^3-9abc+27a^2d \\ T=b^2-3ac \\ Q= \sqrt{(2b^3-9abc+27a^2d)^2-4(b^2-3ac)^3}= \sqrt{S^2-4T^3} \\ C= \sqrt[3]{ \frac{1}{2}(Q+2b^3-9abc+27a^2d)} = \sqrt[3]{ \frac{1}{2}(Q+S)} = \sqrt[3]{ \frac{1}{2} \left ( \sqrt{S^2-4T^3}+S \right )} \\ x_1= - \dfrac{b}{3a}- \dfrac{C}{3a}- \dfrac{b^2-3ac}{3aC} = - \dfrac{b}{3a}- \dfrac{C}{3a}- \dfrac{T}{3aC} \\ x_2= - \dfrac{b}{3a}+ \dfrac{C(1+i \sqrt{3})}{6a}+ \dfrac{(1-i \sqrt{3})(b^2-3ac)}{6aC} \\ ~~~~ = - \dfrac{b}{3a}+ \dfrac{C(1+i \sqrt{3})}{6a}+ \dfrac{(1-i \sqrt{3})T}{6aC} \\ x_3= - \dfrac{b}{3a}+ \dfrac{C(1-i \sqrt{3})}{6a}+ \dfrac{(1+i \sqrt{3})(b^2-3ac)}{6aC} \\ ~~~~ = - \dfrac{b}{3a}+ \dfrac{C(1-i \sqrt{3})}{6a}+ \dfrac{(1+i \sqrt{3})T}{6aC} \\ $

Anonymous

Anonymous Tue 09 Feb 2021 15:11:21 No.12685833 Report

Quoted By:

>>12685777
Begin with the cubic equation:

$ax^3 + bx^2 + cx + d = 0$

Reduce to a depressed cubic,

$\begin{align} y & = x + \frac{b}{3a} \\ p &= \frac{3ac - b^2}{3a^2} \\ q &= \frac{2b^3 - 9abc + 27a^2d}{27a^3} \end{align}$

Our depressed cubic is then

$y^3 + pt + q = 0$ ,

with a rather trivial solution:

$\begin{align} P &= \sqrt{\frac{4p^3}{27q^2} + 1} \\ Q &= \sqrt[3]{\frac{d}{2}} \\ y &= Q\times \left( \sqrt[3]{P - 1} - \sqrt[3]{P + 1}\right) \\ x &= y - \frac{b}{3a} \end{align}$

In OP's problem, we have

$\begin{align} p &= -2 \\ q &= 4 \\ P &= 5\sqrt{\frac{1}{27}} \\ Q &= \sqrt[3]{2} \\ x &= \sqrt[3]{2}\times \left( \sqrt[3]{5\sqrt{\frac{1}{27}} - 1} - \sqrt[3]{5\sqrt{\frac{1}{27}} + 1}\right) \end{align}$

Anonymous

Anonymous Tue 09 Feb 2021 15:33:50 No.12685899 Report

Quoted By: >>12685988

>>12685727

if p is an m-degree polynomial over c, it has a factorization c(z-k1)....(z-km), i.e. it has m roots. if you know exactly how many are real, the rest must be complex. it follows inductively from the fundamental theorem of algebra.

Anonymous

Anonymous Tue 09 Feb 2021 15:56:16 No.12685988 Report

Quoted By:

>>12685899
But how many roots are surreal?

Anonymous

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Anonymous Tue 09 Feb 2021 16:18:01 No.12686073 Report

Quoted By: >>12686761 >>12687993

>>12683023
I

Anonymous

Anonymous Tue 09 Feb 2021 16:44:55 No.12686208 Report

Quoted By: >>12686675 >>12686760

My solution is that I love Kurisu

Anonymous

Anonymous Tue 09 Feb 2021 18:33:16 No.12686675 Report

Quoted By: >>12686760

>>12686208
I got the same solution

Anonymous

Anonymous Tue 09 Feb 2021 18:35:54 No.12686684 Report

Quoted By:

>>12683041
Proof? (I am a brainlet)

Anonymous

Anonymous Tue 09 Feb 2021 18:53:39 No.12686737 Report

Quoted By:

A reminder that if you will ask a lot of questions, your father will try to kill you.

Anonymous

Anonymous Tue 09 Feb 2021 19:03:31 No.12686758 Report

Quoted By:

>>12682939
Nope.

Anonymous

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Anonymous Tue 09 Feb 2021 19:04:18 No.12686760 Report

Quoted By: >>12686939 >>12687173

>>12686208
>>12686675
How to get kurisu gf?

Anonymous

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Anonymous Tue 09 Feb 2021 19:04:45 No.12686761 Report

Quoted By: >>12687875

>>12686073
G

Anonymous

Anonymous Tue 09 Feb 2021 19:58:22 No.12686939 Report

Quoted By:

>>12686760
I'm afraid it involves watching your childhood friend get killed countless times in various horrifying ways.

Anonymous

Anonymous Tue 09 Feb 2021 20:51:03 No.12687173 Report

Quoted By: >>12687200 >>12687270

>>12686760
go for a phd in neuroscience in the best university in america just like kurisu

Anonymous

Anonymous Tue 09 Feb 2021 20:59:08 No.12687200 Report

Quoted By:

>>12687173
but anon, I don't like neuroscience, I $_{\text{like}} \ _{_{\text{controls...}}}$

Anonymous

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Anonymous Tue 09 Feb 2021 21:07:54 No.12687240 Report

Quoted By:

>>12682939

Anonymous

Anonymous Tue 09 Feb 2021 21:12:43 No.12687257 Report

Quoted By: >>12690420

>>12685727
y = x^3 intersects only once and has only 1 real roots and no complex roots

Anonymous

Anonymous Tue 09 Feb 2021 21:16:29 No.12687270 Report

Quoted By: >>12687332 >>12688692

>>12687173
But she didn't have any romantic connections to the men in her university.

That's why she had to get sucked into an insane mad scientist's black hole experiments.

Anonymous

Anonymous Tue 09 Feb 2021 21:35:36 No.12687332 Report

Quoted By: >>12687810

>>12687270
don't give up
you can be the smart okabe who went to the same university and research department as kurisu

Anonymous

Anonymous Tue 09 Feb 2021 23:59:06 No.12687810 Report

Quoted By:

>>12687332
No, that's the path the failure. The only way forward is to take a hostage and recruit a wizard tier hacker and create a time machine.

Anonymous

Anonymous Wed 10 Feb 2021 00:19:09 No.12687875 Report

Quoted By: >>12688665

>>12686761
G

Anonymous

Anonymous Wed 10 Feb 2021 00:50:00 No.12687963 Report

Quoted By:

>>12682939
x^3 = 2x-4
draw the line and cubic
wala

Anonymous

Anonymous Wed 10 Feb 2021 00:59:11 No.12687993 Report

Quoted By:

>>12686073
$\mathbb{I}$

Anonymous

Anonymous Wed 10 Feb 2021 01:48:44 No.12688122 Report

Quoted By:

x = -2, this was insanely easy

Anonymous

Anonymous Wed 10 Feb 2021 05:21:20 No.12688658 Report

Quoted By: >>12688685

>>12684320
No. Do it in the right order. Subtraction comes last.

Anonymous

Anonymous Wed 10 Feb 2021 05:27:12 No.12688665 Report

Quoted By: >>12688693

>>12687875
E

Anonymous

Anonymous Wed 10 Feb 2021 05:27:20 No.12688666 Report

Quoted By:

>>12684320
p.s. It's not suddenly a serial operation once you solve the exponent and multiply. Your calculator is wrong.

Anonymous

Anonymous Wed 10 Feb 2021 05:30:35 No.12688672 Report

Quoted By:

>>12685683
You'd have to be an absolute brainlet to use the qubic formula instead of noticing that -2 is an obvious root and then simply factiring the polynomial with straightforward computation.

If you learned and use the cubic formula, you're more of a computer than a mathematician.

Anonymous

Anonymous Wed 10 Feb 2021 05:30:42 No.12688675 Report

Quoted By:

>>12682939
Engineer cuck here:
Just put it as f(x)=x and calculate it until it converges
ez pz

Anonymous

Anonymous Wed 10 Feb 2021 05:32:29 No.12688681 Report

Quoted By: >>12688687 >>12688892 >>12688904

>>12682939
How many years would it take to just solve this numerically?

Anonymous

Anonymous Wed 10 Feb 2021 05:33:53 No.12688685 Report

Quoted By: >>12690872

>>12688658
retard

Anonymous

Anonymous Wed 10 Feb 2021 05:34:17 No.12688687 Report

Quoted By:

>>12688681
Around 0.0000000000000125 years

Anonymous

Anonymous Wed 10 Feb 2021 05:35:20 No.12688692 Report

Quoted By: >>12688881

>>12687270
That's because they were mostly non-handsome old men and she already got bad experience with one.

Anonymous

Anonymous Wed 10 Feb 2021 05:35:31 No.12688693 Report

Quoted By:

>>12688665
Q

Anonymous

Anonymous Wed 10 Feb 2021 06:59:24 No.12688881 Report

Quoted By:

>>12688692
I thought it was because they were all intimidated by her.

Anonymous

Anonymous Wed 10 Feb 2021 07:02:58 No.12688892 Report

Quoted By:

>>12688681
https://www.google.com/search?q=y%3Dx%5E3%2D2x%2B4

Anonymous

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Anonymous Wed 10 Feb 2021 07:05:28 No.12688899 Report

Quoted By:

>>12682939
yeah, easy peasy,
this is taught in second grade in yugoslavia

Anonymous

Anonymous Wed 10 Feb 2021 07:06:42 No.12688904 Report

Quoted By:

>>12688681
https://www.google.com/search?q=y%3Dx%5E3%2D2x%2B4%2Cx%5E3%2C2x%2D4

Anonymous

Anonymous Wed 10 Feb 2021 15:40:42 No.12689997 Report

Quoted By:

>>12683041
Based

Anonymous

Anonymous Wed 10 Feb 2021 18:08:23 No.12690420 Report

Quoted By:

>>12687257
Wrong, op's polynomial can be written as (x+2)(x-1-i)(x-1+i)

Anonymous

Anonymous Wed 10 Feb 2021 19:24:03 No.12690669 Report

Quoted By:

>>12682939
x3+0=4-2x=03=2x=?????????

Anonymous

Anonymous Wed 10 Feb 2021 20:16:13 No.12690872 Report

Quoted By: >>12691352

>>12688685
> Parentheses
> Exponents
> Multiplication
> Division
> A
> S

What do the last two letter stand for?
Which operation precedes the other?

Anonymous

Anonymous Wed 10 Feb 2021 20:18:23 No.12690880 Report

Quoted By: >>12690894

>>12682939
How can I breed this girl, tell me /sci/.

Anonymous

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Anonymous Wed 10 Feb 2021 20:24:06 No.12690894 Report

Quoted By:

>>12690880
You have to step across.

Anonymous

Anonymous Wed 10 Feb 2021 22:30:41 No.12691352 Report

Quoted By:

>>12690872
double retard

Anonymous

Anonymous Wed 10 Feb 2021 23:24:10 No.12691516 Report

Quoted By:

>>12682939
$\infty$

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