Question

When a particular non-zero integer is substracted from it's square, the result is neither negative nor positive. What is the integer?

Answer 1

The integer that when subtracted from its square results in a value that is neither negative nor positive is zero; however, this contradicts the condition of being a non-zero integer, making it an impossible scenario.

Step-by-step explanation:

The question asks about an integer that when subtracted from its square gives a result that is neither negative nor positive. This occurs only with the integer zero. Let's represent the integer as n. According to the problem, n² - n = 0. If we factor n out of the equation, we get n(n - 1) = 0. There are two solutions to this equation: n = 0 or n - 1 = 0, which leads to n = 1. However, when n = 1 and we substitute it back into the original equation, we get 1² - 1 = 0, which is zero but not a non-zero integer as specified by the question. Hence, the only number that fits the condition of being a non-zero integer and yielding a result of zero when subtracted from its square is zero itself, which is contradictory because zero is not a non-zero integer. Therefore, it is impossible to find a non-zero integer that, when subtracted from its square, equals zero.

Answer 2

If the result is neither negative nor positive, the simplest option is saying that 0 is neither negative nor positive.

For a number to be subtracted from it's square and equal 0, the only possible number is 1.

1 squared is 1, and 1-1=0.