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Help with arithmetic sequence problem

  1. Feb 24, 2009 #1
    The zeros of the polynomial f(x) = x^3 - 33x^2 + 354x + k form an arithmetic sequence. What is the value of k?

    so i let the zeros = a, b, and c. then i did b - a = c - b since it's an arithmetic sequence and they have common differences. so now i have a + c = 2b. i don't know what to do from here. help is much appreciated!
  2. jcsd
  3. Feb 25, 2009 #2


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    Maybe you want four equations because you have four unknowns; although maybe you really have three unknowns (a, b, and k, since you determined c=(2b-a) ).

    (x - a)(x - b)(x - (2b-a)) = x^3 - 33x^2 + 354x + k = 0

    Could you use this, multiply the lefthand side, and then equate the coefficients?
  4. Feb 25, 2009 #3
    oh i see.
    it took a while to multiply out the expression, but i got the answer.
    thanks! :)
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