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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

Look at the projectile motion question: Clearly, the answer is ZERO - its asking for the velocity when it LANDS. If it lands, it's not moving anymore... Who disagrees?

Couldn't understand a word... I was at a complete utter loss... what the hell where they saying?! Ching chang mitsubishi judo teriyaki wang subaru??!! fark!

I found for the following condition: Q = [ bSin(360/b) ] / 2 that Q approaches the value of Pi as b -> ∞ Probably everyone already knows it, but cool nonetheless.

Just wondering

Since the thread called Hardest HSC Exam was closed, and I saw the following post by Templar: http://community.boredofstudies.org/2434595/post-18.html I just had to refute that post, sure, it violates Euclidean geometry, but it does have a solution. The question was: Q1. Given a line of...

Fermat's last theorem was proved by Wiles by first prooving the shimura-taniyama conjecture, however, the final proof was more than 150pages, and it was claimed Fermat had a much more elegant ptoof to his theorem, which stated there are no positive integers which satisfy the following condition...

I was doing some questions on euler's formula when i noticed the following eiπ = - 1 => e2iπ = (- 1)2 .... (squaring both sides) => e2iπ = 1 => ln [ e2iπ ] = ln(1) .... (taking natural logs of both sides) .'. 2iπ = 0 ... (since ln(1) = 0 ) Now, how can 2iπ = 0? Since both i and Pi are a...

It is highly unlike that we need to utilise the General Solution of Cubic equations anytime soon, as its completely out of the syllabus, and creates more working compared to other methods. however, there is a interesting method here which solves cubic equations if coefficient before x2 is zero...

This week, I had to write an English essay on Hamlet and Ros&Guil Are Dead. and how values are the result of contextual interpretations.... It was like an open book test, and we were allowed 3 pages of notes with us to aid our work~ however, it is best to partially remember some of tbe essay...

I have an assessment on trolley and car jacks. We have to write up an engineering report about the data we collected, and work out mechanical advantages etc., trouble is, our data is dodgy, (like how much force is needed to life a 100kg mass on a car jack etc) Are there any resources or sites...

Besides having the lid falling on your fingers, has anyone else experienced any injuries whilst playing on the piano for too much. I spent 6 hours today on a piece, and now I can't even hold a pen :( advice?

Pretty good movie IMO, lots of unexpected twists, good plot and solid acting. Starrs Bruce Willis and Gordon Freeman and some other guy...released 2006 Suggest you go watch it.

Does anyone here play piano just for the fun of it? I played for a year in Yr 8, but stopped for 3 years. Somehow, my interest in piano got reignited and so i just learn various pieces by my self when I have the time. Anyone else here in the same circumstances? I have never taken a test...

Found the following questions quite interesting: 1. Find ii where i = root(-1) 2. The number a is randomly selected from the set {0,1,2,3,...,98,99}. The number b is selected from the same set. What is the probabilty that the number 3a+7b is an 16 digit number?

Can someone please enlighten me on how to actually do this question: Q1. Find ∫(sinmax)/(cosnax) in terms of m, n, Cos(ax) and sin(ax) Help would be appreciated!

SOME WRITING BAND 6 ESSAY TIPS I'll admit this, I suck at English, and I still do. But recently, our school finally broadened our understanding with an Essay Writing Workshop thing - which I found pretty useful for mainstream essay writing across most subjects. Markers sit through tons of...

I have just received my tragic results of my half yearlies and I must say, I am disappointed at my marks. My flu during the exam week was partly to blame for the tradegy. The story: I'm currently ranked in the top twenties in most of my subjects (like 14th, 14th, 17th and a 21th for Ext2...

We all know that it is physically impossible for anything to travel at the speed of light, let alone, faster than the speed of light. But, what about apparent motion? Apparent motion seems to be a very interesting subject, however its very hard to describe in words. (Coz I'm a dumbass) The...

I am having trouble proving the following question: (There were no diagrams for this question!) 1. Let O be the circumcenter of DABC. Suppose AB > AC > BC. Let D be a point on the minor arc BC. Let E and F be points on AD such that AB is perpendicular to OE and AC is perpendicular to OF. Let P...