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Math Help - Polynomial problem

  1. #1
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    Polynomial problem

    I am having difficulty with a particular question, not sure how to approach it (well the chapter in the textbook is on the relation between the roots and coeeficients eg. sums products of roots) so it will use that approach i guess.

    If x^{4}+4x^{3}+mx^{2}+nx+9=(x^{2}+bx+c)^{2} for all values of x, find all possible vales of b and c and the corresponding vales of m and n

    Thanks for your help
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    (x^2+bx+c)^2=x^4+\ldots and identify coefficients.


    Fernando Revilla
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  3. #3
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    this there a way using the sum and products of roots? (ie. sum of roots=-b/a, product of roots =c/a.....etc) just wondering?
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  4. #4
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    Expand the RHS and equate coefficients of like powers of \displaystyle x.
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  5. #5
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by aonin View Post
    this there a way using the sum and products of roots? (ie. sum of roots=-b/a, product of roots =c/a.....etc) just wondering?
    Why?. Expanding the right side and identifying coefficients you'll immediately obtain the parameters.


    Fernando Revilla
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  6. #6
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    alright thanks. yea i thought it would be more complex to solve lols..guess I read too deep into a question?
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