If A = {x : x ∈ ℤ and x² − 4x + 4 = 0}, how many elements are in A?
Advertisement
Answer and explanation
Correct answer: 1
Factor the equation: x² − 4x + 4 = (x − 2)² = 0. Hence x = 2 is the only integer solution. Although the quadratic has a repeated root, a set records each value only once; it does not count multiplicity of roots. Therefore A = {2}, so the set contains exactly one element.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
Factor the equation: x² − 4x + 4 = (x − 2)² = 0. Hence x = 2 is the only integer solution. Although the quadratic has a repeated root, a set records each value only once; it does not count multiplicity of roots. Therefore A = {2}, so the set contains exactly one element.
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.
Advertisement