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Math Help - What must a be greater than for the statement to be true?

  1. #1
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    What must a be greater than for the statement to be true?

    Please help me with this math problem:



    The answer I come to is

    a > (-12-2t)/t^2

    But no matter how I type it in, it says incorrect.
    I also tried a > 0 and a > t and a > -t and so on, just to see if anything is correct, it always says incorrect

    Thank you in advance,
    TheCracker
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  2. #2
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    Re: What must a be greater than for the statement to be true?

    Quote Originally Posted by TheCracker View Post
    Please help me with this math problem:

    The answer I come to is
    a > (-12-2t)/t^2
    Your work is incorrect. You want the discriminate to be negative,
    (2)^2-4a(12)<0
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  3. #3
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    Re: What must a be greater than for the statement to be true?

    You understood the problem incorrectly.You proved the following statement.

    For every t there exists an x such that for every a > x we have at^2 + 2t + 12 > 0.

    Here x may depend on t (think about "every person has a farther": the father depends on the person).So you found an x = (-12 - 2t) / t^2 that depends on t.

    You were supposed to prove the following.

    There exists an x such that for every a > x and for every t we have at^2 + 2t + 12 > 0.

    Here x may not depend on anything; it must be a concrete number. You need to find (the minimal) such number and prove that for every a > x and for every t we have at^2 + 2t + 12 > 0.

    Note that the graph of at^2 + 2t + 12 is a parabola whose branches point up if a > 0 and down if a < 0. In order for the whole graph to be above the x-axis, we must have a > 0 and the equation at^2 + 2t + 12 must have no real roots.
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  4. #4
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    Re: What must a be greater than for the statement to be true?

    Thank you very much !
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