I'm pretty sure they are? Unless that's only certain questions like find the centre of the ellipse given this equation etc.I don't think Ellipses with centre other than O are in the syllabus...
Technically you see them more often in Trials than the actual HSC. They would fall under graph transformations anyway.I don't think Ellipses with centre other than O are in the syllabus...
http://4unitmaths.com/SBHS1986.pdfIs the sequence defined correctly?
Perhaps this was a little difficult for a marathon question, although the needed tools are entirely within the HSC syllabus. I will post a solution a little later to illustrate how some different ideas in calculus interact.
ok so it is defined wrong.
Setting A=2 B=7I keep getting A=1 as the only possible value of A for the polynomial to have real roots.
Either something is seriously messed up with my working or it's surprisingly right.
Nice work, its easier than my method as well, I let the roots be -1, alpha, 1/alpha then used sum of roots, found the quadratic in alpha and discriminant.By inspection -1 is a root, therefore:
Equating co-efficients gives:
Solving the quadratic for real roots gives:
or
Simplifying each one gives:
or
I've actually played around with this result a bit before. I'll post up a question linking heaps of things together, lemme type it up as a continue on from your question if you don't mind.
(Just thought it was a cool result)
Sure go ahead.I've actually played around with this result a bit before. I'll post up a question linking heaps of things together, lemme type it up as a continue on from your question if you don't mind.