Question

Assuming an equation with one side as a squared variable expression and the other side as a numeric expression of zero, such as (x+4)2=0
, which of the following statements is correct?

Hint: How many solutions does (x+4)2=0
have?

(1 point)
Responses

Statement #1: If the numeric expression is zero, there are two solutions.
Statement #1: If the numeric expression is zero, there are two solutions.

Statement #2: If the numeric expression is zero, there is one solution.
Statement #2: If the numeric expression is zero, there is one solution.

Statement #3: If the numeric expression is zero, there are no solutions.
Statement #3: If the numeric expression is zero, there are no solutions.

Answer 1

Statement #2 is correct.

Reason: (x + 4)^2 = 0 implies x + 4 = 0, so x = −4. That's one (distinct) solution — a double root of multiplicity 2, but only one value of x.