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Cubic equation with two unknown coefficients

  1. Feb 27, 2012 #1
    1. The problem statement, all variables and given/known data

    x^3 +px^2 + 56x + q = 0


    I've attempted the first part but I have no idea what to do next. I know usually you'd have 3 new roots inn terms of alpha, beta and gamma but they're not given.

    2. Relevant equations

    Given that the three roots are all positive and are the first free terms of a geometric series with common ratio 2,

    a. find the three roots of the equation.

    b. find the values of p and q.


    3. The attempt at a solution

    I've work out the old roots,

    roots one at a time = -p

    roots two at a time = 56

    product = -q
     
  2. jcsd
  3. Feb 27, 2012 #2

    tiny-tim

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    Hi MegaDeth! :smile:
    (i assume you mean the first three terms? :wink:)

    start by calling the smallest root "r" …

    then you know what the other two roots are :wink:
     
  4. Feb 27, 2012 #3
    Oh god, that's embarrassing. I didn't notice that mistake.

    Ok, so the roots would be: r, r+2 and r+4? If so, how would I use these to find p and q?
     
  5. Feb 27, 2012 #4

    tiny-tim

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    r, 2r, 4r :wink:

    try it, then ask :smile:
     
  6. Feb 27, 2012 #5
    Sorry but I'm not familiar with this method. I don't know how to do it. :(
     
  7. Feb 27, 2012 #6

    tiny-tim

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    well, write out the equations …

    what are they?​
     
  8. Feb 27, 2012 #7

    SammyS

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    What is the method that you're unfamiliar with ?
     
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