Answer: x^2 + 4x - 60 = 0
Step-by-step explanation: Let's assume that the three consecutive integers are x, x+1, and x+2 (where x is the smallest of the three).
According to the problem, the sum of the first integer (which is x) and the product of the other two (which is (x+1)(x+2)) is 62.
We can write an equation based on this information:
x + (x+1)(x+2) = 62
Simplifying this equation, we get:
x + x^2 + 3x + 2 = 62
Rearranging and simplifying further, we get:
x^2 + 4x - 60 = 0
Therefore, the equation that could be used to find the integers is:
x^2 + 4x - 60 = 0