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Finding the number of solutions of an equation

  1. Sep 5, 2009 #1
    1. The problem statement, all variables and given/known data
    Let hk : R -> R where[tex]h_{k}(x)=x^3-6x+k[/tex] and k is a real number

    Find the value(s) of k for which the equation hk has 1,2 or 3 solutions.

    3. The attempt at a solution

    Don't know how to approach this.

    Thanks!!!
     
  2. jcsd
  3. Sep 5, 2009 #2
    Can you graph the function?
    Find max min and do that. It should help.
     
  4. Sep 5, 2009 #3
    Hi,

    Yes, i have graphed the function with the value of k being -8,0,6 and 10 (that was a previous question), but the value k can be anything for this question. How can I find the number of solutions produced?
     
  5. Sep 6, 2009 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    How many times does the graph cross the x-axis? That's the number of solutions.

    Obviously, if k= 0 then the function (not equation) is [itex]h_0(x)= x^3- 6x[/itex] and presumably you are talking about the equation [itex]h_0(x)= x^3- 6x= x(x^2- 6)= 0[/itex] which has 3 solutions, 0 and [itex]\pm\sqrt{6}[/itex]. Now try a few other values of k and see how the graph changes and how many times the graph crosses the x-axis.
     
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