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SOLUTIONS - Terry Lee (1 Viewer)

seanieg89

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Well done on typing solutions Carrot :). I have just a couple of technical issues with the last two qn's that should not matter to most people:

15biii) How do we know that the real root must have multiplicity two?

iv) Should probably consider the case where alpha is real, (although as we have seen, this means that alpha either has a double root at 1 or -1, so does not change the outcome of the calculation).

16) iii) I dont think your argument is valid...perhaps I am misinterpreting what you are saying.

And finally I am unsure if more justification is required for the last one, why does being larger than your two immediate neighbours imply that you are larger than all other P(k)?

Just nitpicking, I don't know how anal BoS are actually going to be.
 

seanieg89

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The reason I stress the cases in iv) is that it is very wrong to think that if alpha and beta are two distinct complex roots of a real quartic, then the roots are alpha, beta, conjugate of alpha, conjugate of beta. This is only necessarily the case if alpha and beta are NOT real. The reason why this question still works out okay is that the symmetry of coefficients forces a pretty rigid structure on any real roots that P can have.
 

Carrotsticks

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Thanks Sean, going to start addressing them now. A cup of coffee does wonders.

Hop on FB perhaps, much easier that way.
 

Zeroes

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I'm hoping my assessment mark will pull me up to an E4 but HSC mark may be just below. I think cutoff is around 65% going from raw marks database.
 

brianphamm

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Hey Carrot, are you sure the height of the rectangle is bounded to x^2 + y^2 = r^2? Since it's on an angle, would it be different? (question is 14c)
 

Life4Never

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Hey Carrot, are you sure the height of the rectangle is bounded to x^2 + y^2 = r^2? Since it's on an angle, would it be different? (question is 14c)
Thats correct as the height of the rectangle is the y value of the circle at each value of x.

dx is so small there is no difference if its "sloped" as exaggerated in the diagram if thats what you are trying to say.
 

lolcakes52

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looking at a 70-80, maybe a bit over 80. With 14a, I split it into 3x^2+4/x(x^2+4) + 4/x(x^2+4). Im not sure if that was valid but I thought I got the answer in the exam.
 

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