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Factor Theorem Problem

  1. Oct 1, 2006 #1
    This is the problem:

    A quadratic function f(x) with integral coefficients has the following properties: [tex]f(3/2)=0[/tex], (x-2) is a factor of f(x), and f(4) = 50. Determine f(x).

    The answer in the back of the book is [tex]f(x)=5(2x-3)(x-2)[/tex]

    I can easily understand the (2x-3) and (x-2), but I don't understand the "5", and "f(4) = 50".
    Last edited: Oct 1, 2006
  2. jcsd
  3. Oct 1, 2006 #2


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    f(4) = 50 means that the quadratic function evaluated at x = 4 has a value of 50. Your final solution must satisfy this condition as well as the others.

    Hint, the "5" probably has something to do with that last criterion.
  4. Oct 2, 2006 #3
    Hmm, when you sub f(4) = 50 in f(x)=(2x-3)(x-2)

    You end up with 50=10

    Am I on the right track towards implementing that "5" into my final equation?
    Last edited: Oct 2, 2006
  5. Oct 2, 2006 #4


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    Which tells you that f(x) is NOT (2x-3)(x-2)!

    But you also know that 2x-3 and x- 2 are the only factors involving x.
    What happens if you substitute x= 4 into f(x)= A(2x-3)(x-2) where A is a constant?
  6. Oct 2, 2006 #5
    One word to describe HallsofIvy.. Brilliant!

    You end up with A=5, thanks I understand it now :D
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