[MATHEDCC] Hi-tech math continued

Phil Mahler (mahlerp@admin.middlesex.cc.ma.us)
Thu, 18 Sep 1997 16:51:34 EST5EDT4,M4.1.0,M10.5.0

>For all of the trinomials the class made up (at random over [-10,10]]),
>find the ratio of
>factorable trinomials to non-factorable trinomials and discuss the
>probability that a trinomial that is randomly generated is factorable. How
>does the question change if the coefficients come from a wider range of
>integers, -100 to 100, for example?

So, is there an easy answer to this question? (Obviously assuming factoring
over the integers.) I have seen this question discussed somewhere.

Is this equivalent to finding the probablility that, given three random
integers a,b,c in a range, that b^2 - 4ac is a perfect square? Or to the
probability that, given three random integers a,b,c, in a range, there
exist integers m and n such that mn = ac, and m+n = b?

Phil Mahler
Middlesex CC
Bedford, MA
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