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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsMediumLevel 5

If A = {x ∈ ℤ : x² − 4x + 5 = 0}, choose the correct conclusion about A.

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Answer and explanation

Correct answer: A = ∅

Complete the square: x² − 4x + 5 = (x − 2)² + 1. For every integer, and indeed every real number, (x − 2)² is at least zero, so the expression is at least 1. It can never equal zero. Therefore, the equation has no integer solution and the set A contains no elements; hence A = ∅.

Tags

setsempty setintegersquadratic 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 = ∅

Why is this the correct answer?

Complete the square: x² − 4x + 5 = (x − 2)² + 1. For every integer, and indeed every real number, (x − 2)² is at least zero, so the expression is at least 1. It can never equal zero. Therefore, the equation has no integer solution and the set A contains no elements; hence A = ∅.

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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