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Mathematics: Post your doubts here!

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if x-y is a factor of a polynomial and if you use substitute y in the differential equation of the polynomial does the answer have to be zero?? Why?
 
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Someone help me with this S1 problem. It's from O/N/13 - 61. I solved it (attached the picture) - my distribution for X is wrong; can someone please explain why the distribution for X is lower than that for Y? I attached the markscheme screenshot too, haha. Please help!
Screenshot (468).png
Screenshot (469).png
 

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  • 2015-04-30 05.00.02.jpg
    2015-04-30 05.00.02.jpg
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z=9 e^i(1/3)

z=9(e^0(cos(1/3)+i sin(1/3))

square root of z=(9 (e^0(cos(1/3)+i sin(1/3)) )^1/2

=9^(1/2)( cos(0.5*(1/3 π))+i sin(0.5*(1/3 π)) )

=+-3(cos(1/6 π) + i sin(1/6 π))

one square root is =3(cos(1/6 π) + i sin(1/6 π))
= (3√3/2)+i (3/2) (open the bracket)
r=3
θ=1/6 π

so 3 e^i (1/6) π

other root = - 3(cos(1/6 π) + i sin(1/6 π))
= - (3√3/2)- i (3/2)
r=3
θ = (1/6 π)
θ= (1/6 π)-π = -(5/6)π

so 3 e^i (-5/6) π
 
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