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Math Help - Upper and Lower Bounds

  1. #1
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    Aug 2009
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    St. Charles, MO
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    Upper and Lower Bounds

    Hey everybody, I'm new to this forum.
    But down to business.
    I just started taking an honors math class this year called "Honors Math Analysis".

    So anyway... The problem I'm having right now is..

    "Use synthetic division to verify the upper and lower bounds of the real zeros of F"

    67.) f(x) = x^4 - 4x^3 + 15
    Upper Bound: x = 4 ; Lower Bound: x = -1

    I'm pretty confused as to what I'm doing..
    She goes really fast and leaves no time at the end of the day to ask questions, and then does not go over the homework the next day for feedback..

    This might be the wrong forum.. So I think I'm going to post this in the pre-calc forum.
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  2. #2
    Newbie
    Joined
    Aug 2009
    Posts
    13
    "If you do synthetic division by a positive number a, and every number in the bottom row is positive or zero, then a is an upper bound for the roots, meaning that all the real roots are ≤ a.

    If you do synthetic division by a negative number b, and the numbers in the bottom row alternate sign, then b is a lower bound for the roots, meaning that all the real roots are ≥ b."

    I had to Google to find that.
    I think it reveals how to solve the problem as long as you know how to perform synthetic division.
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