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- Feb 14, 2012

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This is another interesting problem that I tried to work on it with no luck so far to break the code...

Problem:

Find the number of real order pairs of $(y, a)$ that satisfy \(\displaystyle 100y^3-3\left( 150+\frac{a}{8} \right)y^2+3\left( 125+\frac{5a}{8} \right)y-3\left( \frac{59a}{96}-\frac{75}{2} \right)=0\) such that $0 \le y \le 2.5$.

At first glance, my mind draws a blank and this is not good because whenever this happens to me, chances are I will not be able to solve the problem. And here I am now, asking for a modicum of help or ideas to crack this problem.

Thanks.