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Math Help - Factoring this quadratic

  1. #1
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    Factoring this quadratic

    \displaystyle f(x)=-4.9x^2+19.6x+58.8

    I'm a little confused as using the quadratic formula would leave me with x=6 and x=-2, but (x-6)(x+2) does not equal the original function.
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  2. #2
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    Multiplying out will give you x^2-4x-12 and if you multiply this by a factor of -4.9 you get the original f(x) you had.
    You could also do this the other way, you are looking for roots to the equation f(x)=0 so you get -4.9 x^2 +19.6x+58.8=0. Divide through by 4.9 and you get the equation I gave above.
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  3. #3
    Super Member Quacky's Avatar
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    If we assume that f(x)=0

    Then we assume that: -4.9x^2+19.6x+58.8=0
    My -4.9 times table is a little rusty, so allow me to tidy this up a little:
    -49x^2+196x+588=0
    Times both sides by -1:
    49x^2-196x-588=0
    Divide both sides by 49:
    x^2-4x-12=0
    (x-6)(x+2)=0
    x=6 or x=-2

    If you substitute those back into the original function, you will find that they give a solution of f(x)=0.

    If f(x)=0, then 4.9f(x)=0 too. Did you follow why?

    Edit: Beaten again!
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