AS level further maths

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#1
Im learning about roots of polynomials rn, and I was wondering if you've gotta know the identities for the roots of a cubic and quartic off by heart? And if so whats a good way to remember them?
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1 month ago
#2
(Original post by Danny boii)
Im learning about roots of polynomials rn, and I was wondering if you've gotta know the identities for the roots of a cubic and quartic off by heart? And if so whats a good way to remember them?
Do you mean things like sums and products of roots in terms of coefficients? I wouldn't expect you to remember them for cubics and quartics, but they're fairly easy to work out
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1 month ago
#3
(Original post by Danny boii)
Im learning about roots of polynomials rn, and I was wondering if you've gotta know the identities for the roots of a cubic and quartic off by heart? And if so whats a good way to remember them?
Yeah sadly you do, they're not given to you in the formulae booklet.
I struggle to remember them off by heart as well, but I've found that you can easily recognize a pattern or something that will help you remember what comes next.
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1 month ago
#4
The general formula is: coeff of is times the sum of products formed by choosing k roots.

e.g.
coeff of is - "sum of 1-term products" e.g. (cubic) or (quartic)
coeff of is:+"sum of 2-term products" e.g. or
coeff of is: - "sum of 3-term products" e.g. or

and so on.

[Note: choosing is done without repetition - there are no terms like ].
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