If Z = {x ∈ Z : (x − 1)(x + 2) = 0}, what is the correct roster form of Z?
Answer and explanation
Correct answer: Z = {−2, 1}
A product is zero when at least one of its factors is zero. Therefore, solve x − 1 = 0 or x + 2 = 0. The first equation gives x = 1, while the second gives x = −2. Both values are integers and satisfy the original equation: (1−1)(1+2)=0 and (−2−1)(−2+2)=0. Thus the roster form is {−2, 1}; order does not matter in a set, so A is correct.
Frequently asked questions
What is the correct answer to this question?
Z = {−2, 1}
Why is this the correct answer?
A product is zero when at least one of its factors is zero. Therefore, solve x − 1 = 0 or x + 2 = 0. The first equation gives x = 1, while the second gives x = −2. Both values are integers and satisfy the original equation: (1−1)(1+2)=0 and (−2−1)(−2+2)=0. Thus the roster form is {−2, 1}; order does not matter in a set, so A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
