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July 17th, 2015, 09:29 AM  #1 
Banned Camp Joined: Jul 2015 From: Germany Posts: 8 Thanks: 0  Essay on Cubic polynomial ?????
So for my Extended essay, I might wanna do something about different ways of solving cubic function. I decided to demonstrate the general formula method, the cardano's method and the trigonometric and hyperbolic method for cubic polynomial. I will then compare different approach and evaluate them ( their pros and cons. ) However, it is not sparkling and unique enough to get an A. Therefore, I might have to add something to my essays. Here are some ideas. 1, Imaginary coefficient of cubic polynomial. 2, use of newton's method. (Can it approximate polynomial with complex coefficient as well ? ) 3, Application of cubic polynomial in real life ( Practical Purposes ) which one do you think is good ? After all of these, would my essay be intact ? Is it a good topic. ? I am now petrified. And my research question would be ( An exploration on cubic function: Different means of solving it and its piratical purpose ) Is it OK? Too board ?? Thank you for reading and I would be elated if you can reply. ( anything that you are up to, plzz tell me, it might really help me ) 
July 17th, 2015, 09:37 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
What level are you writing at? My answers would be very different depending on how much you have studied. Also, how long is the essay? What practical purposes are you thinking of using as examples for #3? Unless the paper is long I think it would be better to focus on a relatively narrow aspect and cover it completely, rather than touch on many aspects in brief. 
July 17th, 2015, 10:09 AM  #3 
Banned Camp Joined: Jul 2015 From: Germany Posts: 8 Thanks: 0 
My essay is quite a long essay. 4000 words for international baccalaureate ( extended essay ). Would that be adequate, i mean the topics that I just mentioned ?

July 17th, 2015, 10:19 AM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
I think the basic idea of comparing/contrasting three different methods of solving the cubic is good. If I understand correctly, your 2nd suggestion is to add a fourth method, NewtonRaphson, to the mix and to additionally describe its applicability to complex roots and/or polynomials. I don't really understand your other two suggestions, though. For #1, what would you talk about, exactly? ("i appears in the formula" doesn't fill many of the 4000 words.) For #3, I don't know what sort of thing you would include, or if you just hope to find something (a tenuous hope when you're writing an essay). There are other things you could add, of course. General information on rootsolving (bisection, secant, etc.); polynomial rootfinding (e.g., Schonhage's method); numerical stability (how different are the roots if you perturb the input coefficients slightly), and so forth. 
July 20th, 2015, 03:03 AM  #5 
Banned Camp Joined: Jul 2015 From: Germany Posts: 8 Thanks: 0  Thanks
Thank you so much for your reply. P.S. why are there so many Korean posts and comments on the website ? 
July 20th, 2015, 03:03 AM  #6  
Banned Camp Joined: Jul 2015 From: Germany Posts: 8 Thanks: 0  Quote:
 
July 20th, 2015, 05:49 AM  #7 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  

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