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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsEasyLevel 6

What is A = {x ∈ ℤ : x is even and x² = 2x}?

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Answer and explanation

Correct answer: A = {0, 2}

Solve the equation x² = 2x by bringing all terms to one side: x² − 2x = 0, so x(x − 2) = 0. Hence x = 0 or x = 2. Both values are integers, and both are even because each is divisible by 2; zero is also an even integer since 0 = 2 × 0. Therefore, the required set is A = {0, 2}.

Tags

setseven integerssolution setquadratic equationThe Empty SetFinite and Infinite SetsEqual Setsthe empty set finite and infinite sets equal setsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

A = {0, 2}

Why is this the correct answer?

Solve the equation x² = 2x by bringing all terms to one side: x² − 2x = 0, so x(x − 2) = 0. Hence x = 0 or x = 2. Both values are integers, and both are even because each is divisible by 2; zero is also an even integer since 0 = 2 × 0. Therefore, the required set is A = {0, 2}.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.

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