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Pat's Parabola Permutations

Pat Bellew poses this nice parabola permutation problem: Here is an interesting excursion to try; take a quadratic equation that you know has rational roots, and then permute the values of A, B, and C through all possible variations. What is the probability that they would ALL have rational roots? Read his post at: http://pballew.blogspot.com/2011/10/permuations-of-coefficents-in-quadratic.html I even like the question: so that each permutation has roots!