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I am referring to the statements, not the numbers.

'I. the polynomial must cut the x-axis at least once' is correct if we consider x as real. So 'II. if P(alpha) = 0, then P(conj. alpha)=0' is not correct. II is correct if we consider x as complex. So I is not correct. .: the statements are mutually exclusive.

http://www.itute.com/2010/12/10/free-download-2010-nsw-bos-mathematics-extension-1-solutions/

typo z^3+1

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simple and easy to understand answer by considering energy: more fuel, greater height reached, greater kinetic energy when the rocket falls back to earth, .: greater speed.

This method of finding the rational roots works only when they exist. It works for most of the questions in textbooks because the questions were prepared for it to work, i.e. rational roots were used to construct the polynomials. Just think about this: does a polynomial always cross the x-axis...

wording of the question 10 times longer than the original means 11 times the original?

what degree is z^4 =(z-1)^4?

are you referring to my answer?

z=1+(sqrt3)i

hope you know the meaning of 'equivalent'

to illustrate the point further, sketch both functions and see they are the same

you are right, they cannot be equivalent if they have different domains

they are not equivalent, hope you know why

ln [ Ax / ( sqrt(x^2 +1) )] not= ln [ A sqrt [ (x^2) / (x^2+1) ]]

itute.com has the solutions

the locus of w is the Im axis, perhaps without the origin O

(1-α^2)(1-β^2)(1-γ^2)(1-δ^2) =(1-α)(1-β)(1-γ)(1-δ)(1+α)(1+β)(1+γ)(1+δ) =(1+q+r+s)(1+q-r+s) :spin:

You've got the right answer. Care to share your solution method?