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State the number of complex roots,possible number of real roots and possible rational roots for x^5 - x^3 - 11x^2+ 9x+18=0

  • Math - ,

    there are 5 possible rational and real roots. Given the wording of the problem, though, it's likely that there are some complex roots, reducing the number of real candidates.

    There may be 2 or 4 complex roots, meaning that there may be 5,3, or 1 real root.

    Lacking any further information, all the real roots may be rational, and in fact will be integers.

    A little synthetic division shows that we have no rational roots.

    In fact, there are no real roots greater than 0 or less than -1. So, there are 4 complex roots and one real root -1 < r < 0

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