To determine the number of integers x that have the property that x^2 is non-positive, we need to consider the values of x for which x^2 is less than or equal to zero.
A non-positive value means a number that is either negative or zero. Therefore, we need to find the values of x for which x^2 is negative or zero.
1. When x is 0, x^2 = 0. So, x = 0 is a valid solution.
2. For negative integers, when x is any negative number (such as -1, -2, -3, and so on), x^2 will always be positive because the product of two negative numbers is positive. Therefore, negative integers do not have the property that x^2 is non-positive.
3. For positive integers, when x is any positive number (such as 1, 2, 3, and so on), x^2 will always be positive because the product of two positive numbers is positive. Therefore, positive integers do not have the property that x^2 is non-positive.
In summary, there is only one integer, which is 0, that has the property that x^2 is non-positive.