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FM question to do with coefficients and roots

i cantthinkofany

Hi guys,It's a question from CIE A level further maths, I can do the first part of the question and also can find S3, but I am not sure how to calculate S-2. The examiner report says that S3 = 3 and S-2 = 1 Any help would be greatly appreciated. Thanks! :smile:

:smile:

9231 S03 qp1.png15.2KB

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Original post by i cantthinkofany

Hi guys,It's a question from CIE A level further maths, I can do the first part of the question and also can find S3, but I am not sure how to calculate S-2. The examiner report says that S3 = 3 and S-2 = 1 Any help would be greatly appreciated. Thanks! :smile:

:smile:

Use the deduced equation to find what the sums and products of its roots are (remember; they're not simply

\alpha,\beta,\gamma

anymore)

S_{-2}=(2\alpha+1)^{-2}+(2\beta+1)^{-2}+(2\gamma+1)^{-2}

=\frac{1}{(2\alpha+1)^{2}}+\frac{1}{(2\beta+1)^{2}}+\frac{1}{(2 \gamma+1)^{2}}

=

\frac{\sum(2\alpha+1)^{2}(2\beta+1)^{2}}{(2\alpha+1)^{2}(2\beta+1)^{2}(2\gamma+1)^{2}}

...and you can work from there.

Further hints:

Spoiler

(edited 7 years ago)

If you are trying to find

S_n

then you could make the substitution say

z=y^n

, then to find the value of

S_n

you would just be looking at the coefficient of the second term of the polynomial.
So to find

S_2

if you let

z=y^2

and then rearrange and form a polynomial equation, and look at the second term coefficient, that will be the sum

S_2

, so it will be

-b/a

where's is coefficient of first term and b is coefficient of second term.

i cantthinkofany

OP

Hey guys, thanks for the reply. Both of the methods seem like valid ways to do it!

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