Danny boii
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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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davros
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(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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confuzzledteen
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(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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DFranklin
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The general formula is: coeff of x^{N-k} is (-1)^k times the sum of products formed by choosing k roots.

e.g.
coeff of x^{N-1} is - "sum of 1-term products" e.g. -(\alpha+\beta+\gamma) (cubic) or -(\alpha+\beta+\gamma+\delta) (quartic)
coeff of x^{N-2} is:+"sum of 2-term products" e.g. \alpha\beta+\beta\gamma+\gamma \alpha or  \alpha\beta + \beta\gamma+\gamma \delta+\delta\alpha + \alpha \gamma + \beta\delta
coeff of x^{N-3} is: - "sum of 3-term products" e.g. -\alpha\beta\gamma or -(\alpha\beta\gamma+\beta\gamma \delta+\gamma\delta\alpha + \delta\alpha\beta)

and so on.



[Note: choosing is done without repetition - there are no terms like \alpha^2\beta].
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