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

• Sep 24th 2012, 11:36 AM
TheCracker
What must a be greater than for the statement to be true?

http://imageshack.us/a/img441/7181/clipboard01hb.jpg

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 :(

TheCracker
• Sep 24th 2012, 11:51 AM
Plato
Re: What must a be greater than for the statement to be true?
Quote:

Originally Posted by TheCracker
http://imageshack.us/a/img441/7181/clipboard01hb.jpg
The answer I come to is
a > (-12-2t)/t^2

Your work is incorrect. You want the discriminate to be negative,
$(2)^2-4a(12)<0$
• Sep 24th 2012, 12:02 PM
emakarov
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.
• Sep 24th 2012, 12:03 PM
TheCracker
Re: What must a be greater than for the statement to be true?
Thank you very much ! :)