2005 Q8 (4 Viewers)

[who_loves_maths]

Originally Posted by withoutaface
The propositions were:
a) A number that is not the root of any polynomial with integer coefficients.
b) A number that is not the root of any polynomial with rational coefficients.

Any polynomial indicates any polynomial; equation, expression or otherwise.

^ yeah but that's just the point. it is NOT just ANY polynomial, equations or expressions...

because like i said, rational and integer polynomial expressions are NOT equivalent... whilst rational and integer polynomial equations are equivalent.

i understand that you still do not see the point i have tried to make, but it doesn't matter to me anymore, i am confident of what i know over this issue now. there's not much more that can be said over this, so you can have the last word if you want...

 

[Dumsum]

P(x) = x/2 + 1
G(x) = x + 2

P(x) = (x+2)/2
= G(x)/2

Therefore, if a number α is not a zero of G(x), it's also not a zero of P(x).

Here's what I think: withoutaface, when you say "Any polynomial with rational coeffecients can be expressed as one with integer coefficients by multiplying both sides by the product of the denominators," I think it's more correct to say "Any polynomial with rational co-efficients can be expressed in terms of one with integer co-efficients."

who_loves_maths:
Even though the two polynomials are not equivalent (choose a number, say 1, P(1) doesn't equal G(1)), I'm inclined to say that it is SUFFICIENT to say a transcendental number is a number which is not a zero of any polynomial with integer co-efficients.

 

[Affinity]

2001 we had irrationality of e.
2003 we had irrationality of pi.

What shall we have in 2005?

prove that the HSC is irrational

 

[KFunk]

I think that one's given.

 

[lum]

wholovesmaths, r u srsly in yr 12? damn, u know a lot... but then again, i'm SURE i dun wanna do maths in uni now, not after these discussions... u guys seem a bit... queer, no offence

 

[NT-social]

hehe

prove that the HSC is irrational

... thats a good one(can u believe dis is my first ever reply,since registering @ dis site, and for what? lol

 

[haboozin]

wholovesmaths, r u srsly in yr 12? damn, u know a lot... but then again, i'm SURE i dun wanna do maths in uni now, not after these discussions... u guys seem a bit... queer, no offence

WLM, you tend to cover up your idendity, do not tell anyone what school you go to etc.

What are you affraid of?

 

[Dumsum]

WLM, you tend to cover up your idendity, do not tell anyone what school you go to etc.

What are you affraid of?

All those internet stalkers that lurk on this site.

 

[haboozin]

All those internet stalkers that lurk on this site.

I'm yet to see a stalker with a fettish of a maths nerd.

 

[flower_farie]

Uh, r normal HSC students suppose to understand what that actually meant (the stuff on the first page) cauz i never got taught that im im really scared that some ppl actually know what that stuff means