Question

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

Answer 1

To solve the equation \( x(x+2) = 0 \), we need to find the values of \( x \) that make the product equal to zero. According to the zero product property, if \( ab = 0 \), then either \( a = 0 \) or \( b = 0 \).

In this case, we have:

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

Thus, the solutions to the equation are \( x = 0 \) and \( x = -2 \).

Now, let's analyze the options provided:

- **Zavier states that only \( x = -2 \) makes the function equal to 0.** This is incorrect because he ignores \( x = 0 \).

- **Boaz states that both \( x = 0 \) and \( x = -2 \) make the function equal to 0.** This is correct as both values satisfy the equation.

- **Sophie states that only \( x = 0 \) makes the function equal to 0.** This is also incorrect because she ignores \( x = -2 \).

Based on this analysis, the correct explanation is given by:

**Option #2: Boaz.**