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    May 2012
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    Hong Kong
  1. When it says "choose a root and draw line segments from this root to the other two roots" and then do the same for z^4 and z^5 does it mean that we're joining lines from 1 point to the other points?
  2. Yes, you are on the right track. The roots are equally spaced around the unit circle. So the distance between any two roots is the same. Using the same method of finding the distances between roots when n = 3,4,5,6,7,8, you just need to do the same but using the variable "n". Hope I helped. Thanks for helping! I've got an idea on how to do it I have a question on proving, is it necessary to start at k=1 for mathematical induction? Or is there any other way to prove the conjecture?
  3. I've just started the IA I've came up with some values of the distance between the roots when n=3,4,5,6,7,8 They are decimal numbers, I'm not sure if I'm on the right track and I have difficulty in finding the pattern and forming an equation do you guys have any advice for me?? Thanks!
  4. Hey guys, so after you've found the solution to the general 2x2 How should this be used to prove the parabola it looks strange if im just putting the solution there without using it for anything.. any guide?
  5. so after we have done the matrix and got 0 0 0 0 we can use the other two to find the line that the planes intersect? is this line part of the proof? why? there is a lot of things that im not sure.. i am really not good at math..
  6. Is that part of matrix?? I don't get this and I think I should learn it now.. what do you mean let z=t where t is a Real parameter? Where should I start learning about this? And for part B I have found the solution to the general 2x2 system but I'm not sure of how to use this to prove the graphical pattern.. What I did was using the vertex form, substituting a point that passes the pattern formed into the vertex form.. finding what a is and therefore finding the equation of the graph then i just put the graph with the family of lines and prove it graphically saying that it's a horizontal parab
  7. For the 3x3 I have just found that the bottom row are all zeros.. is that not enough? I still have to look for the line that the 3 planes intersect?
  8. I took Additional Maths IGCSE and didn't learn RREF. I guess you didn't learn it in GCE either. You probably don't need to express it in parameters then. Just give final equations, it might do. Yeah it is. In other words, it's the solution of the system. Yeah last bullet point you can prove that. Any graphical pattern, really. You can prove that it's horizontal parabola. Yes you need to find the equation first. Don't ask how, go through this whole thread and you'll find the answer. Thanks, is it not necessary to mention the equations of the straight lines that the 3 planes intersect? I am qui
  9. I have learnt some basics from the GCE syllabus and I am able to prove my conjectures using matrix but I don't get the parameter part.. and I can't really see this in the matrix chapter in my book.. is that used to find out the equation of the straight line which the three planes intersect? And about the last bullet point, am I going to prove that it is a horizontal parabola? Do I have to look for the equation of that parabola first or what? Thanks for everyone who had helped.. thankyou so much!
  10. and what is the use of writing the the system in the y=ax+b form? Merged actually we haven't even done matrix.. I just read the book and learnt part of it myself I dont even know what is parameter
  11. what's the meaning of use the other two equations as parametrics? I havent learnt vectors yet, can anything tell me whats the use of doing that??
  12. I have read through the whole thread but still I'm stuck with the last two bullet points.. What does it mean by setting up a 2x2 system the incorporates the pattern? Does it mean that I have to create another 2x2 linear equation or what ? Can anyone please help!
  13. Im stuck at finding recursive formula and discrete mathematical model I tried using excel but i have no clue about what's going on can anyone give me a guide or tips on that??
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