# FM question to do with coefficients and roots

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#1
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!
1
3 years ago
#2
(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!
Use the deduced equation to find what the sums and products of its roots are (remember; they're not simply anymore)

=

...and you can work from there.

Further hints:
Spoiler:
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Remember that:

and

2
3 years ago
#3
If you are trying to find then you could make the substitution say , then to find the value of you would just be looking at the coefficient of the second term of the polynomial.
So to find if you let and then rearrange and form a polynomial equation, and look at the second term coefficient, that will be the sum , so it will be where's is coefficient of first term and b is coefficient of second term.
4
#4
Hey guys, thanks for the reply. Both of the methods seem like valid ways to do it!
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