What is the roster form of W₁ = {x : x ∈ ℤ and x² = 2x}?
Answer and explanation
Correct answer: W₁ = {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, x = 0 or x = 2. Both are integers and therefore satisfy the domain restriction. The set is consequently W₁ = {0, 2}. Dividing by x would incorrectly discard the valid solution x = 0.
Frequently asked questions
What is the correct answer to this question?
W₁ = {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, x = 0 or x = 2. Both are integers and therefore satisfy the domain restriction. The set is consequently W₁ = {0, 2}. Dividing by x 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.
