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Math Help - General question about comparing coefficients

  1. #1
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    General question about comparing coefficients

    Hi I know that if

    ax^2 + bx + c = dx^2 + ex + f

    then a=d, b=e and c=f

    but how do we know this?

    Of course it seems intuative but does it need to be proved?

    Thanks!
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  2. #2
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    Re: General question about comparing coefficients

    this is only true if ax + bx + c = dx + ex + f for all x (or in fact just for some values, see why below)
    Replacing x by 0 you find that c=f. So ax+bx=dx+e.
    Now replacing x by 1 we have a+b=d+e. X by -1 we have a-b=d-e. Adding those 2 equations we have 2a=2d so a=d. Substract them so b=e.
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