Zavier, Boaz, and Sophie are trying to find the values of x that make the following quadratic function equal 0: x(x+2)=0

Question

. Each student came up with a different answer, which they explained in the options. Which student’s explanation is correct?

Option #1: Zavier says that only x=−2
will make the function equal 0, and he provided the given work: −2⋅(−2+2)=−2⋅(0)=0
.

Option #2: Boaz says that the values x=0
and x=−2
will both make the function equal 0, and he provided the given work: 0⋅(0+2)=0⋅(2)=0
, and −2⋅(−2+2)=−2(0)=0
.

Option #3: Sophie says that only x=0
will make the function equal 0, and she provided the given work: 0⋅(0+2)=0⋅(2)=0
.

(1 point)
Option #
is the correct explanation.
Remaining Attempts : 3

Answer 1

To solve the quadratic equation \( x(x+2) = 0 \), we can use the zero-product property, which states that if the product of two factors is zero, at least one of the factors must be zero.

The factors in this equation are:

1. \( x = 0 \)
2. \( x + 2 = 0 \) which simplifies to \( x = -2 \)

This means that both \( x = 0 \) and \( x = -2 \) are solutions to the equation \( x(x+2) = 0 \).

Now, let's analyze the students' explanations:

• Zavier claims that only \( x = -2 \) is a solution, which is incorrect because he ignores \( x = 0 \).
• Boaz correctly identifies both \( x = 0 \) and \( x = -2 \) as solutions. His explanation includes both calculations, which validates his answer.
• Sophie claims that only \( x = 0 \) is a solution, which is incorrect for the same reason as Zavier.

Since Boaz correctly includes both solutions, the correct option is:

Option #2: Boaz's explanation is correct.