The product of two integers is #75# and their sum is #-28#. What are the two integers?

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Answer 1 · 2015-07-10T23:32:32

#-3# and #-25#

Let the integers be #m# and #n# with #abs(m) <= abs(n)#

Since #mn = 75# is positive, #m# and #n# are either both positive or both negative.

If #m# and #n# were both positive, then #m + n# would be positive too, but #m + n = -28#, so #m# and #n# are both negative.

#75 = 3 * 5 * 5#

so #(m, n)# must be one of:

#(-1, -75)#, #(-3, -25)#, #(-5, -15)#

Of these only #(m, n) = (-3, -25)# gives us #m + n = -28#