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Math Help - cubic polynomial

  1. #1
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    cubic polynomial

    The cubic polynomial f(x) is such that the coefficient of x^3 is 1 and the roots of f(x) = 0 are k, 2k and  (1 - k), where  k > 0. It is given that f(x) has a remainder of 30 when divided by (x - 1).
    Show that 2k^3 - 3k^2 + k - 30 = 0
    I do not quite understand the question so I don't know where to start from.
    I only know that f(1) = 30
    Does 'root' here mean factor?
    Would that mean that f(x) = (k)(2k)(1 - k)? But that doesn't make much sense to me because I don't see how 2k^2 - 2k^3 has any connection with anything.

    I'm sorry for the silly question and any help would be really really appreciated. Thank you in advance.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by caramelcake View Post
    I do not quite understand the question so I don't know where to start from.
    I only know that f(1) = 30
    Does 'root' here mean factor?
    Would that mean that f(x) = (k)(2k)(1 - k)? But that doesn't make much sense to me because I don't see how 2k^2 - 2k^3 has any connection with anything.

    I'm sorry for the silly question and any help would be really really appreciated. Thank you in advance.
    f(x)=(x-k)(x-2k)(x-(1-k))

    CB
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  3. #3
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    Thank you! The question is surprisingly simple now
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