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Find all real and complex zeros of h(x)

  1. Oct 29, 2013 #1
    1. The problem statement, all variables and given/known data
    It's asking me to find all the real and complex zeros of the function x^3 + 2x^2 - 16.


    2. Relevant equations



    3. The attempt at a solution
    I have tried factoring the first 2 terms and i come up with x2(x+2) - 16 but I don't know where to go from there. Any help would be appreciated.
     
  2. jcsd
  3. Oct 29, 2013 #2

    Mark44

    Staff: Mentor

    This is not really a very good start. Instead you should see if you can find a number r such that x3 + 2x2 - 16 = (x - r) * (x2 + lower degree terms).

    The Rational Root Theorem (you can search for this on the web) says that if r is a root of your cubic polynomial, it has to be a number that evenly divides -16. The only candidates are ±1, ±2, ±4, ±8, and ±16. Does your textbook mention this theorem? Does your textbook show any examples of similar problems? Do you read your textbook?
     
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