If O = {x : x ∈ Z and x² = 2x}, what is the correct roster form of O?
Answer and explanation
Correct answer: O = {0, 2}
Solve the defining equation x² = 2x by bringing all terms to one side: x² − 2x = 0. Factoring gives x(x − 2) = 0. By the zero-product property, either x = 0 or x − 2 = 0, so x = 2. Both values are integers, as required. Hence the roster form is O = {0, 2}. Dividing by x at the beginning would incorrectly discard the valid solution x = 0.
Frequently asked questions
What is the correct answer to this question?
O = {0, 2}
Why is this the correct answer?
Solve the defining equation x² = 2x by bringing all terms to one side: x² − 2x = 0. Factoring gives x(x − 2) = 0. By the zero-product property, either x = 0 or x − 2 = 0, so x = 2. Both values are integers, as required. Hence the roster form is O = {0, 2}. Dividing by x at the beginning would incorrectly discard the valid solution x = 0.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
