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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsMediumLevel 4

What kind of set is A = {x : x ∈ N, x² + 2x + 1 = 0}?

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Answer and explanation

Correct answer: Empty set

Factor the equation as x² + 2x + 1 = (x + 1)² = 0. Its only real and integer solution is x = −1. However, −1 is not a natural number, so it does not satisfy the restriction x ∈ N. Consequently, no permitted value belongs to A, which means A = ∅, the empty set.

Tags

setsempty-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?

Empty set

Why is this the correct answer?

Factor the equation as x² + 2x + 1 = (x + 1)² = 0. Its only real and integer solution is x = −1. However, −1 is not a natural number, so it does not satisfy the restriction x ∈ N. Consequently, no permitted value belongs to A, which means A = ∅, the empty set.

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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