Identify the set A = {x ∈ ℝ : x² + 4 = 0}.
Answer and explanation
Correct answer: A is the empty set
For every real number x, x² is non-negative, so x² + 4 is at least 4 and can never equal zero. Equivalently, solving the equation gives x² = -4, which has no real solution. Although complex numbers ±2i solve the corresponding equation in the complex number system, the domain here is ℝ, so they are not elements of A. Hence A = ∅.
Frequently asked questions
What is the correct answer to this question?
A is the empty set
Why is this the correct answer?
For every real number x, x² is non-negative, so x² + 4 is at least 4 and can never equal zero. Equivalently, solving the equation gives x² = -4, which has no real solution. Although complex numbers ±2i solve the corresponding equation in the complex number system, the domain here is ℝ, so they are not elements of A. 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.
