If B = {x ∈ Z : x² = 2x}, what is B?
Answer and explanation
Correct answer: English: B = {0, 2} | हिन्दी: B = {0, 2}
Move 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, which gives x = 2. Both solutions are integers and therefore satisfy the stated domain. Checking confirms that 0² = 2·0 and 2² = 2·2. Thus B = {0, 2}, so option A is correct. The solution x = 0 must not be lost when dividing by x.
Frequently asked questions
What is the correct answer to this question?
English: B = {0, 2} | हिन्दी: B = {0, 2}
Why is this the correct answer?
Move 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, which gives x = 2. Both solutions are integers and therefore satisfy the stated domain. Checking confirms that 0² = 2·0 and 2² = 2·2. Thus B = {0, 2}, so option A is correct. The solution x = 0 must not be lost when dividing by x.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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