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Math Help - real zeros of a polynomial function

  1. #1
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    real zeros of a polynomial function

    real zeros of a polynomial function-theorem-bounds-zero1b.png

    real zeros of a polynomial function-theorem-bounds-zero1c.png


    i understand how four was found. i dont understand how 8/3 was found.
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  2. #2
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    a_0= -\frac{1}{3}, a_1= \frac{1}{3}, a_2= -\frac{4}{3}, a_3= \frac{5}{3}, and a_4= -\frac{1}{3} again.

    Taking absolute values, |a_0|= \frac{1}{3}, |a_1|= \frac{1}{3}, |a_2|= \frac{4}{3}, |a_3|= \frac{5}{3}, and |a_4|= \frac{1}{3} so we really only have three different values, \frac{1}{3}, \frac{4}{3}, and \frac{5}{3}.

    The largest (max) of those is \frac{5}{3} so 1+ max(|a_0, a_1, a_2, a_3, a_4) is 1+ \frac{5}{3}= \frac{3}{3}+ \frac{5}{3}= \frac{8}{3}.

    The difference between the two is that in the first one, you add all the fractions, to get 4, then take the larger of 1 and 4. In the second, you take the largest of the fractions, then add 1 to that.
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  3. #3
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    Quote Originally Posted by nando29 View Post
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    i understand how four was found. i dont understand how 8/3 was found.

    The maximum of \{\left|-\frac{1}{3}\right|,\left|\frac{5}{3}\right|, etc.\} is \frac{5}{3} , and this added to 1 gives \frac{8}{3}

    Tonio
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  4. #4
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    thank you very much!
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