Question

Two consecutive integers have a product of 132.Find the integers

Answer 1

The difference between consecutive integers is 1.
Let x = smaller integer.
Then x + 1 is the next greater consecutive integer.

x(x + 1) = 132

x^2 + x - 132 = 0

(x + 12)(x - 11) = 0

x + 12 = 0   or   x + 11 = 0

x = -12   or   x = -11

Since x is the smaller of the two integers, the answers are:
-12, -11
11, 12
There are two pairs of such integers.