Which option is correct for A = {x ∈ ℝ : x² + 2x + 2 = 0}?
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Answer and explanation
Correct answer: A = ∅
Complete the square: x² + 2x + 2 = (x + 1)² + 1. For every real x, (x + 1)² is at least zero, so (x + 1)² + 1 is always at least one and can never equal zero. Equivalently, the discriminant is 2² − 4(1)(2) = −4, which is negative. Hence there is no real solution and A is the empty set.
Frequently asked questions
What is the correct answer to this question?
A = ∅
Why is this the correct answer?
Complete the square: x² + 2x + 2 = (x + 1)² + 1. For every real x, (x + 1)² is at least zero, so (x + 1)² + 1 is always at least one and can never equal zero. Equivalently, the discriminant is 2² − 4(1)(2) = −4, which is negative. Hence there is no real solution and A is 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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