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Math Help - using a polynomial equation

  1. #1
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    using a polynomial equation

    Any help will be greatly appreciated

    An envelope is 4cm longer then it is wide. The area is 96 sq. cm Find the length and width. Use a polynomial equation.
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  2. #2
    Senior Member Peritus's Avatar
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    <br />
\begin{gathered}<br />
  S_{envelope}  = w(w + 4) = 96 \hfill \\<br />
  w^2  + 4w - 96 = 0 \hfill \\ <br />
\end{gathered}

    solve the quadratic equation to obtain the solution
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  3. #3
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    am i doing this correctly?
    w-12=0
    +12 +12
    w=12

    w+8=0
    -8 -8
    w=-8
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  4. #4
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    Quote Originally Posted by imbadatmath View Post
    am i doing this correctly?
    w-12=0
    +12 +12
    w=12

    w+8=0
    -8 -8
    w=-8
    Plug your numbers in back into the original equation for Area and see. Hint: Remember that width, length, cannot be negative.
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  5. #5
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    would it be
    12(12+4)=96
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  6. #6
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    12*(12+4)= 12*16 =192 so that's cant be right.

    the factoring of your polynomial should be (x-8)(x+12) which gives you x-8 = 0 or x+12 = 0, meaning x=8 or x=-12. Since x is a length and cant be negative the answer must be x=8.

    Does it work?

    8*(4+8) = 8*12 = 96!
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  7. #7
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    so what i was doing before
    w-12=0
    +12 +12
    w=12

    w+8=0
    -8 -8
    w=-8
    was going in the total wronge direction?
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  8. #8
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    No, it is just that your signs were backwards.

    (w-8)(w+12) = w^2 + 4w - 96

    where as

    (w+8)(w-12) = w^2 - 4w - 96

    Notice that the first quadratic equation is the one you are working with. The second equation above is similar to the first but the middle w-term is negative when it should be positive.
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