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In the following second order equation $ax^2+2bx+1.5=0$ where $a$ and $b$ are given by random points $(a,b)$ in the $[0,2]\times[0,1]$ rectangle what is the probability of having two real solutions?

I'm a little lost here. I tried integrating $4b^2-6a$ with $0\leq a \leq2$ and $0\leq b\leq 1$ as limits but the integral comes up negative. I created a simulation of the problem using matlab and the probability is 0.11 but I want to find a way to solve it on paper and not with using matlab.

Any thoughts?

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    Please don't crosspost (answer accepted at link): http://stats.stackexchange.com/questions/25661/probability-that-a-quadratic-equation-with-random-coefficients-has-two-real-solu2012-04-01

2 Answers 2