The sum of a nonzero integer and zero has the same value as the square of the integer.What is the integer?
not just an answer.
A.-2
B.-1
C.0
D.1
E.2
x+0 = x^2
x^2 - x = 0
x(x-1) = 0
x = 0 or x = 1, but x was to be a non-zero integer
so x = 1
To find the integer that satisfies the given condition, let's analyze the statement.
The sum of a nonzero integer and zero has the same value as the square of the integer.
Let's say the integer is "x." We can write the given condition as an equation:
x + 0 = x^2
Since adding zero to any number does not change its value, we can simplify the equation to:
x = x^2
Now, we can solve this equation to find the possible values for "x":
x^2 = x
Rearranging the equation, we have:
x^2 - x = 0
Factoring out an "x," we get:
x(x - 1) = 0
Now, we can use the zero-product property, which states that if the product of two factors is zero, then at least one of the factors must be zero:
x = 0 or x - 1 = 0
Solving for "x," we find two possible values:
x = 0 or x = 1
So, the integer that satisfies the given condition is either 0 or 1. Therefore, the correct answer is:
D. 1