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Solving Polynomal Equations

  1. Feb 21, 2007 #1
    1. The height,length and width of a small box are consecutive intergers with the height being the smallest of the three dimensions. If the length and width are increased by 1 cm each and the height is doubled, then the volume is increased by 120 cm^3. Find the dimensions of he original small box



    2. v=lwh



    3. I tried to appoach this two different ways but couldn't get either to work:

    1. h = x
    w = x+1
    l= x+2
    therefore (2x)(x+2)(x+3) = 120
    2x^3 + 10x^2+12x-120 = 0
    i tried to use the factor theroem to solve the equation but could not get it to work.
    p{+-1,+-2,+-3...}
    q{+-1,+-2}
    p/q {+-1,+-1/2, +-2, +-3, +-3/2...}

    I knowthat in order to solve the question, I am going to need to need to find the roots of the polynomial and therefore have to solve for x. The factor theroem indicates that if i plug in p/q into the above given equation, it will equal zero, and i can finish the question. The only problem i am having is determining which p/q value satisfies the equation. Another solution would be to factor, but i tried that and it ended up being..

    2x^2(x+5) + 12(x-10) and since there are no more common factors, it cannot be taken any further. As a result, i am pretty sure i have to use the factor theorem, but i can't figure out what p/q value satisfies the equation

    So then i tried (2x)(x+2)(x+3)= 120 + (x)(x+1)(x+2)
    and got..
    x^3+7x^2-10x-120 = 0
    and tried to use factor theorem again but couldn't get it to work.


    Thanks in advance for the help.
     
    Last edited: Feb 21, 2007
  2. jcsd
  3. Feb 21, 2007 #2
    That second equation is what you need to solve. You made some sort of algebra mistake when you expanded, the answer is a nice integer
     
  4. Feb 21, 2007 #3

    cristo

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    Staff Emeritus
    Science Advisor

    Your second method is correct. You have made a mistake in your last line though; it should read x^3+7x^2+10x-120 = 0.

    Try and find a factor here (it shouldn't take too many tries!) Note that you do not need to try negative values, since x is a length, and a negative length is not physically valid.
     
  5. Feb 21, 2007 #4
    ok i see it now, can't believe i had negative 10x..thanks for the help
     
  6. Feb 21, 2007 #5

    AlephZero

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    Science Advisor
    Homework Helper

    That's correct.

    Check your algebra. The "-10x" is wrong.
     
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