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Thread: Polynomials question

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    Polynomials question

    For roots of a polynomial stuff, do you have to remember like alpha^2 + beta^2 + gamma^2 + delta^2 and what this is equivalent to? I know alpha^2 + beta^2 = (alpha+beta)^2 - 2alpha*beta but do we have to remember the hard ones like shown above? If we do is there a way to derive them?
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    Re: Polynomials question

    Well you could form a polynomial with roots alpha^2, beta^2, gamma^2, delta^2. And then finding the sum of roots (-b/a) of that polymomial
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    Re: Polynomials question

    Quote Originally Posted by pikachu975 View Post
    For roots of a polynomial stuff, do you have to remember like alpha^2 + beta^2 + gamma^2 + delta^2 and what this is equivalent to? I know alpha^2 + beta^2 = (alpha+beta)^2 - 2alpha*beta but do we have to remember the hard ones like shown above? If we do is there a way to derive them?




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    Re: Polynomials question

    Quote Originally Posted by InteGrand View Post




    Ah thanks for that, didn't know this works for more than three terms
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    Re: Polynomials question

    Quote Originally Posted by InteGrand View Post




    Is there a formula for the sum of cubes? Thanks for this
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    Re: Polynomials question

    Quote Originally Posted by pikachu975 View Post
    Is there a formula for the sum of cubes? Thanks for this
    yes

    i derived it from scratch during my honours year... a fun exercise
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    Re: Polynomials question

    Quote Originally Posted by pikachu975 View Post
    Is there a formula for the sum of cubes? Thanks for this


    https://en.wikipedia.org/wiki/Newton's_identities .

    As background reading too, you may want to see:

    - https://en.wikipedia.org/wiki/Symmetric_polynomial

    - https://en.wikipedia.org/wiki/Elemen...ric_polynomial (and this part: https://en.wikipedia.org/wiki/Elemen...ic_polynomials (which was asked as a question by glittergal96 in a previous MX2 Advanced Level marathon here: HSC 2016 MX2 Marathon ADVANCED (archive))).
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    Re: Polynomials question





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    Re: Polynomials question

    Is there any way to do all this stuff using pythagorus? I mean with all the a^2, b^2

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    Re: Polynomials question

    Quote Originally Posted by fluffy54324 View Post
    Is there any way to do all this stuff using pythagorus? I mean with all the a^2, b^2
    uhhh good pattern recognition, but pythagoras is for triangles/orthogonality only
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    Re: Polynomials question

    Why thankyou my good sir. I tip my hat to you

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