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Re: HSC 2014 4U Marathon Product of roots > 0 as c<0 Case #1: all 3 roots are real and positive (trivial case) Case #2: 2 of the roots are a complex conjugate pair and the other being real and positive (assuming a,b,c are integer coefficients) Note* when you multiply a complex conjugate pair...

Re: MX2 Integration Marathon

Re: MX2 Integration Marathon xsin(ln(x))+C reverse product rule

Re: HSC 2014 4U Marathon

Re: MX2 Integration Marathon mind the misuse of integral

Re: MX2 Integration Marathon

Re: MX2 Integration Marathon easier than I thought

Re: MX2 Integration Marathon

Re: MX2 Integration Marathon

Re: MX2 Integration Marathon Rushed this one, hopefully no errors

Re: MX2 Integration Marathon Very nice integral :D

Re: HSC 2014 4U Marathon Felt so dumb after I realised how to do this :(

the 2nd question makes no sense(the equation of the circle) and is the first question: Let P(x1, y1) and Q(x2, y2) be two points on the ellipse with equation x^2/a^2 + y^2/b^2 =1 such that PQ is a focal chord.Let the normals at P and Q meet at R and M. M is the middle point of the chord PQ. (a)...

Just a tip, with a sketch, you would of been able to determine one of the tangents straight away (y=-2)

m8 u knew i just woke up from my nap :(

misread my b, I should of wrote 2 times the sum of adjacent sides squared

Hi nen

Re: HSC 2014 4U Marathon Forgot about this question (forgot an 'up' after concave). I didn't include the other scenario when f(b)≤f(a) but either way it should still yield the same result

Here's a guided sample solution to solving, factorising (both in the real and complex fields) of z^5-1=0. This method is the same as the textbooks. (Sidenote: different schools use different methods; this one is the most common.) If you have any questions on what I did feel free to ask :p

Re: MX2 Integration Marathon 2. which makes sense cause the positive area cancels the negative area :)