stupidness (1 Viewer)

[mazza_728]

so incredibly lost .. .brain has totally shut down.

 

[abdooooo!!!]

Originally posted by freaking_out
yep, once u've done either 3u or 4u polynomials that is.

polynomials? hahaha... i still remember my 4u polynomial lesson at school last term, it took 15mins for my teacher to write down all the formulas and thats it, a whole topic finished.

edit: that teacher is a genius... cambridge graduate... he does division of polynomials in his head in 1 or 2 seconds.

 

[KeypadSDM]

Originally posted by ND
Just to get you more excited, i'll post up another method :

w^3-1=0
the roots of this eqn are 1,w,w^2 (you're allowed to write this without proof)
and the sum of roots of this eqn is 0 (as the coefficient of w^2 is 0).
.'. w^2+w+1=0

Let's move onto something interesting with the cube roots of unity ...

How about, what are the possible values of w^2k + w^k + 1?

Where k is a positive integer.

Muhuhahahahaha (Ahem ... 2003 4 unit HSC 8a.)

 

[ND]

Originally posted by KeypadSDM
Let's move onto something interesting with the cube roots of unity ...

How about, what are the possible values of w^2k + w^k + 1?

Where k is a positive integer.

Muhuhahahahaha (Ahem ... 2003 4 unit HSC 8a.)

Heheh i remember this one, it was the 1st question i did.
w^3=1
w^3k-1=0
(w^k-1)(w^2k+w^k+1)=0
so then w^k=1, meaning that w^2k+w^k+1=(w^k)^2+w^k+1=3
also it can equal 0. Hmm i think there was another value as well (i remember there being 3 in the exam), but i'm about to go out and so my brain is not really in maths mode. I'll come back to it tomorrow if it's still unsolved.

 

[Constip8edSkunk]

0 and 3 are the only solutions

 

[Angstyprincess]

hmm..this should all be very familiar to me..shouldnt it..

 

[ND]

Originally posted by Constip8edSkunk
0 and 3 are the only solutions

Yeh you're right.