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Cubic Equation

  1. Nov 9, 2008 #1
    1. The problem statement, all variables and given/known data
    Suppose 'a' and 'b' are real numbers such that the roots of the cubic
    equation ax^3-x^2+bx-1=0 are all positive real numbers. Prove that:
    i) 0<3ab<=1
    ii) b>= 3^0.5

    2. Relevant equations
    Let x,y,z be the roots:

    3. The attempt at a solution
    I differentiated the above function. For the function to have three
    distinct roots. the differentiated function (quadratic) should have 2
    distinct roots. I put the discriminant >=0 to get part i.

    But I cannot understand what shall I do with part ii?

    I also noticed that the graph of the equation at x=0 is -1.
    Help me further!
  2. jcsd
  3. Nov 9, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    Actually, nothing is said about the three roots being distinct- only that then are positive real numbers.
  4. Nov 9, 2008 #3
    So Did I do the first on by the wrong method??
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