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Math Help - Upper bound/Lower bound?

  1. #1
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    Upper bound/Lower bound?

    Ok, I know how to start this problem, but the synthetic division is confusing me a little.

    Use synthetic division to verify the upper and/or lower bounds of the zeros of f.
    f(x) = 2x^4 - 8x + 3
    Upper bound: x = 3; Lower bound: x = -4

    So the possible real zeros I think are:
    plus or minus 1/2, plus or minus 1.5

    Now, I am confused. Can anyone help?
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by tsmith View Post
    Ok, I know how to start this problem, but the synthetic division is confusing me a little.

    Use synthetic division to verify the upper and/or lower bounds of the zeros of f.
    f(x) = 2x^4 - 8x + 3
    Upper bound: x = 3; Lower bound: x = -4

    So the possible real zeros I think are:
    plus or minus 1/2, plus or minus 1.5

    Now, I am confused. Can anyone help?
    Unfortunately, our math write capabilities do not allow for synthetic division. I could do it though.

    Are you have a problem with the synthetic division itself, or the upper and lower bound concept?
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  3. #3
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    I am having trouble with how to set up the synthetic division. Like what numbers I use.
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by tsmith View Post
    Like what numbers I use.
    You use 3 and -4. Because this is what you are given. So,

    3 | 2 +0 +0 -8 +3
    ____+6+18+54+138__
    __ _2 6 18 46 141

    Now, from the upper and lower bound rule, you can confirm that 3 is an upper bound because all of the numbers in thel ast row (6,18,46,141) are all positive.

    Does this help you?
    Last edited by VonNemo19; September 13th 2009 at 11:39 AM.
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  5. #5
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    This is extremely helpful. So now I do the synthetic division for -4, right?
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  6. #6
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by tsmith View Post
    This is extremely helpful. So now I do the synthetic division for -4, right?
    Right, but remember that the rule for the lower bound is different.
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  7. #7
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    Smile

    I completely understand. Thank you so much for your help.
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  8. #8
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by tsmith View Post
    I completely understand. Thank you so much for your help.
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