Good Polynomial Revision Question (1 Viewer)

[hyparzero]

Let P(x) = x²+ax+b , where a and b are real.

i) Resolve P(P(x))-x into two quadratic factors

ii) Find a relationship between a and b which ensures all roots of P(P(x)) - x are real.

iii) Hence or otherwise, solve the equation (x²-3x+1)²-3(x²-3x+1)+1-x = 0

 

[hyparzero]

No attempts? you're ALL a bunch of WUSSY SILLY NANNIES!

geez..

 

[housemouse]

Well I can tell you that I have no idea cause Im not sure what the first part says.

 

[Sober]

Are you sure that quadratic can be factorised?
I even plugged this into mathematica and it gave me nothing:

Factor[(x^2 + ax + b)^2 + a(x^2 + ax + b) + b - x]

 

[Affinity]

i) (x^2 + (a-1)x + b)(x^2 + (a + 1)x + a+b+1)
ii) (a-1)^2 - 4b > 0 and (a+1)^2 - 4(a+b+1) > 0
iii) x = 1+sqrt(2), 10sqrt(2),2 + sqrt(3) and 2 - sqrt(3)

and no.. I haven't seen it before.

hint for part 1.. a fixed point of a function f, is a point x such that f(x)=x

No attempts? you're ALL a bunch of WUSSY SILLY NANNIES!

geez..

now here's one for you: f(x) = x^2 - 2x + 2
find f^2006 ( x) that is f(f(f....f(f(x))

another one:
z = cos(a*pi) + i sin(a*pi), where a is real.
if z^n =/= z for all n>1, prove that a is not rational

 

[haque]

i) (x^2 + (a-1)x + b)(x^2 + (a + 1)x + a+b+1)
ii) (a-1)^2 - 4b > 0 and (a+1)^2 - 4(a+b+1) > 0
iii) x = 1+sqrt(2), 10sqrt(2),2 + sqrt(3) and 2 - sqrt(3)

and no.. I haven't seen it before.

hint for part 1.. a fixed point of a function f, is a point x such that f(x)=x


now here's one for you: f(x) = x^2 - 2x + 2
find f^2006 ( x) that is f(f(f....f(f(x))

another one:
z = cos(a*pi) + i sin(a*pi), where a is real.
if z^n =/= z for all n>1, prove that a is not rational

Affinity i'll have a gho at the other one after ive finished my hsc exams but here's the first one

f(x)=(x-1)^2+1
f^2(x)=((x-1)^2+1-1)^2+1=(x-1)^4+1 and a pattern emerges with parallels to gp series
f^n(x)=(x-1)^2^n +1 so just sub in value of n=2006 and u get the answer
f^2006(x)=(x-1)^2^2006 +1

 

[haque]

No attempts? you're ALL a bunch of WUSSY SILLY NANNIES!

geez..

Not everyone visited or saw ur post-besides its not good to be so arrogant(Affinity just honed u)-after ur done with affinity's q u can attempt one of mine-mind u it is simple

integral infinity to 0 e^-x^2dx express as exact value

 

[idling fire]

Egad...

i) (x^2 + (a-1)x + b)(x^2 + (a + 1)x + a+b+1)
ii) (a-1)^2 - 4b > 0 and (a+1)^2 - 4(a+b+1) > 0
iii) x = 1+sqrt(2), 10sqrt(2),2 + sqrt(3) and 2 - sqrt(3)

How on Earth did you do that...??? *falls over (anime style!!!)*
I'm so lost for everyone else's questions too... sigh.

 

[haque]

(Sorry if i wasn't meant to do the q-i tried to delete it but i couldn't)Affinity could u give me some advice on what books/ tutorials i could use or where i could get my hands on them for uni-like the type of maths done in actuarial?(i asked in actuarial forum-none replied)

 

[Raginsheep]

If you want "Actuarial Mathematics" will suit you nicely

 

[haque]

If you want "Actuarial Mathematics" will suit you nicely

Lol thanx-not too good with words, don't like english-could u give me some advice cos apparently unsw is different to maq when it comes to the maths done in the first year

 

[Raginsheep]

No, what I meant was that "Actuarial Mathematics" is a textbook for maths done in actuarial studies.

I really don't think theres that great deal of difference. Dare I say it but UNSW might be slightly harder than Macq but I've only skimmed through the Macq course outlines so I can't really say.

But http://www.bookshop.unsw.edu.au/bookweb/details?ITEMNO=9780938959465 is what you want. Its a mother of a text book though.

 

[KeypadSDM]

Not everyone visited or saw ur post-besides its not good to be so arrogant(Affinity just honed u)-after ur done with affinity's q u can attempt one of mine-mind u it is simple

integral infinity to 0 e^-x^2dx express as exact value

It's a shame you screwed it up:
e^-x^2dx = exp(-2x) not exp(-x^2).

 

[haque]

Sorry Keypad-i'm not familiar with the notation here-u knew what i meant tho

 

[haque]

No, what I meant was that "Actuarial Mathematics" is a textbook for maths done in actuarial studies.

I really don't think theres that great deal of difference. Dare I say it but UNSW might be slightly harder than Macq but I've only skimmed through the Macq course outlines so I can't really say.

But http://www.bookshop.unsw.edu.au/bookweb/details?ITEMNO=9780938959465 is what you want. Its a mother of a text book though.

Thanx Raginsheep-just a q do i need to learn extra stuff before i get into it?(like finish off first year caclulus as done in uni etc etc or are there specific maths courses?)

 

[Raginsheep]

I haven't actually read the book so I wouldn't know but for at least the first few chapters most likely no.

UNSW and Macq (I think) have specific maths courses for actuarial students but there quite similar to regular maths anyways. Just more depth, ordering changes and slight differences in topics.

 

[haque]

Thanx man-u've been really helpful, cleared a lot of things for me(unlike my careers adviser who was useless)

 

[Raginsheep]

lol........what exactally did you ask him/her. Most career advisors wouldn't really know bout this sort of stuff.

 

[haque]

i guess so-but he told me that there were no scholarships at all available for actuarial-lol i look at the coop booklet and there's one and i see one at macquarie-but our careers adviser's a real bludger but he's a funny guy