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(s+1)(s+2)^2 I wouldn't call it hard.

Now we can go back to fullonoob's question, modify it a bit and get more interesting ones by just removing some terms. This actually makes the question much harder and much more interesting: Solve 1. 4x^3 + 5x^2 + 2x - 20 = 0 2. 4x^3 + 2x - 20 = 0 3. 4x^3 + 5x^2 - 20 = 0 4. x^4 + 5x^2 +...

Somewhat uglier, but equivalent expressions from wolframalpha.com yield the four roots, the last two of which are the complex roots:

I started a thread on this stuff a few years ago at <a href="http://community.boredofstudies.org/238/extracurricular-topics/99063/cubics-quartics.html">http://community.boredofstudies.org/238/extracurricular-topics/99063/cubics-quartics.html</a> , and that was one of the questions in that...

It's a bit boring though. See if you can solve x^4-x-13=0 exactly. (The 1969 3 unit paper asked for the approximate solution to this using Newton's method, but you can actually solve it exactly.)

You could do a substitution. Let y=x^2+2x So y^2+y=x^4+4x^3+5x^2+2x Hence x^4+4x^3+5x^2+2x-20=y^2+y-20=(y-4)(y+5)

(x^2+2x-4)(x^2+2x+5)=0 So x=-1\pm\sqrt5 or -1\pm2i For the other one, the double root will be a root of the derivative, so 3x^2+3p=0 and x^2=-p. So q^2=(-(x^3+3px))^2 q^2=x^6+6px^4+9p^2x^2=-p^3+6p^3-9p^3=-4p^3 So q^2 + 4p^3 = 0

At this stage it is suggested that NSW can keep their HSC. However there were some concerns raised in The Age newspaper yesterday about the new draft K-10 syllabus released on Monday by ACARA and attached below. This does not augur well for any proposed 11-12 syllabus, since this K-10 syllabus...

My submission for the document in question is at http://www.angelfire.com/ab7/fourunit/submission3.pdf I would also recommend Bill Pender's submission which he gave me permission to reproduce at http://www.angelfire.com/ab7/fourunit/0806BOSSubmission.pdf I have also set up a new website at...

I did a thread on the syllabus development at http://community.boredofstudies.org/238/extracurricular-topics/110007/syllabus-development.html The draft document you seek is at http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/mathematics-extension-2-st6-draft.pdf There is a...

I have been advised that unfortunately the HSC solutions book might not be ready by Feb 27, but it will be mailed out when it is ready. Sorry about that.

If you don't know the fundamental theorem of calculus, perhaps I should put it another way. Do you prove Pythagoras' Theorem every time you use it?

There's no need to prove Euler's formula every time you use it. Do you prove the fundamental theorem of calculus every time you calculate an integral?

But you don't have to be stupid just because your teacher is stupid.

(r(\cos x+i\sin x))^n=(re^{ix})^n=r^ne^{ixn}=r^n(\cos nx+i\sin nx) Then let n=3. And if anyone says but that's not in the syllabus, tell them it should be.

It's free for members, $35 for non-members.

On Saturday, Feb 27, 2010 at Macquarie University's Macquarie Theatre, there will be the Examiners' Day for the 2009 HSC and SC maths exams. So if you want to go to get info on the marking of these exams, be there at 8:45am. It goes till about 3:55pm. You can usually also get a copy of the...

Not if it is inferior to what we already have.

<b><font size="+3">January 27, 2010</font></b> <b>Day 1 of NOT implementing the new syllabus</b> Well we were told that the new syllabus is to be implemented in 2010. And then we were told it isn't. Then we were told it will be implemented in 2011. And then we were told it isn't. Do...

Yes. To make comparisons to the old 4 unit course easier (which ran from 1966-1980), I've attached a pdf of the contents section of Coroneos' Level 1 books. I've also attached a pdf of the contents section of an even older book by Coroneos on the Leaving Certificate Mathematics I Honours course...