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
.

Answer 1

Boaz is correct.

Reason: x(x + 2) = 0 implies a product is zero, so at least one factor must be zero. Thus x = 0 or x + 2 = 0 → x = −2. Both x = 0 and x = −2 make the expression 0 (as shown by the provided substitutions).