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Math Help - Descartes' Rule of Signs Help

  1. #1
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    Descartes' Rule of Signs Help

    I need help figuring out this problem:

    Use Descartes' Rule of Signs to analyze the number of positive and negative real roots and the number of non-real roots of the function:

    There are at least __ and at most ___ positive real roots.
    There are at least___ and at most___ negative real roots.
    There are at least ___and at most ____ non-real roots.
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  2. #2
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    Quote Originally Posted by badandy328 View Post
    I need help figuring out this problem:

    Use Descartes' Rule of Signs to analyze the number of positive and negative real roots and the number of non-real roots of the function:

    There are at least __ and at most ___ positive real roots.
    There are at least___ and at most___ negative real roots.
    There are at least ___and at most ____ non-real roots.
    The coeficients of h(x) change sign 3 times, hence there are at most 3
    positive roots of h(x) . As the number of positive roots can only change by
    multiples of 2 the minimum number of real roots is 1.

    The coefficients of h(-x) change sign 6 times, thus there are at most 6
    negative roots of h(x) , and the minimum number is 0.

    As 3+6=9 and there are a total of 9 real or non-real roots there may be as
    few as 0 non-real roots. The maximum number is 8 (when there is one real
    root).

    RonL
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