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HSC 2013 MX2 Marathon (archive) (1 Viewer)

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Sy123

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Re: HSC 2013 4U Marathon

It's as if this thread is invisible to everyone besides the usual bosers. Usually you'd have some other randoms participate in marathon threads.
:( - its probably the questions. And that I answer them too fast not giving a chance for others.

Ok, next time someone posts a normal type question I will leave it for others to answer it so the participation rate is too high.
So yeah if someone could post a question that would be great, if I answer it I won't post the answer straight away (unless it is a difficult one and I somehow manage to find it)
 
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Re: HSC 2013 4U Marathon

A question that is a little easier to other people don't get scared off or anything:





(it isn't that long if you can create shortcuts for yourself.)
did you get something like 2x^3+3x^2+8=0? just wanted to check, probably made heaps of sillies along the way.
 

GoldyOrNugget

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Re: HSC 2013 4U Marathon

Sy posted that easy polynomial roots question at the bottom of pg 27, that's definitely approachable by any 4u student, and no one else's tried it yet... weird
 

Sy123

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Re: HSC 2013 4U Marathon

did you get something like 2x^3+3x^2+8=0? just wanted to check, probably made heaps of sillies along the way.
Yeah something like that, I only remember that the first 2 terms were 2, 3 and co-efficient of x was 0. So yeah good enough lol.

How did you do it?
 

Sy123

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Re: HSC 2013 4U Marathon

Still not what I meant, the lim should be on the side of the cosines.
Well I did have the 3 dots implying that it continued to infinity after the nth term, but I will change it again (even though no-one else will answer it)
 
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Re: HSC 2013 4U Marathon

Yeah something like that, I only remember that the first 2 terms were 2, 3 and co-efficient of x was 0. So yeah good enough lol.

How did you do it?
Edit: cbb to latex, will scan solution
 
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RivalryofTroll

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Re: HSC 2013 4U Marathon

Polynomials Question:

If alpha, beta and gamma are roots of the equation:

x^3 - px - q = 0

Find the equation whose roots are alpha/(beta.gamma), beta/(alpha.gamma), gamma/(alpha.beta).



NOTE: Sorry, I don't use latex.
 
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Re: HSC 2013 4U Marathon

A question that is a little easier to other people don't get scared off or anything:





(it isn't that long if you can create shortcuts for yourself.)
damn I think I missed all the shortcuts :(


 
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HeroicPandas

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Re: HSC 2013 4U Marathon

Polynomials Question:

If alpha, beta and gamma are roots of the equation:

x^3 - px - q = 0

Find the equation whose roots are alpha/(beta.gamma), beta/(alpha.gamma), gamma/(alpha.beta).



NOTE: Sorry, I don't use latex.
x^3 - px - q = 0

Roots:



We want equation with: alpha/(beta.gamma), beta/(alpha.gamma), gamma/(alpha.beta).

Re-arranging product of roots and subbing into ^

New aim is to find eqn with roots:

Let y= x^2/q

x= sqrt(yq) -> sub this into the original equation: x^3 - px - q = 0

THEREFORE:

Chuck the q over and square both sides



 
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RealiseNothing

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Re: HSC 2013 4U Marathon

Let me change the question to make the value a bit more specific:



Find
 
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