Choose the correct statement about A = {x ∈ ℝ : x² - 2x + 5 = 0}.
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Answer and explanation
Correct answer: A = ∅ (the empty set)
Complete the square: x² - 2x + 5 = (x - 1)² + 4. For every real number x, (x - 1)² is at least zero, so the expression is at least 4 and can never equal zero. Therefore, the equation has no real solution, and the set of its real solutions is empty: A = ∅.
Frequently asked questions
What is the correct answer to this question?
A = ∅ (the empty set)
Why is this the correct answer?
Complete the square: x² - 2x + 5 = (x - 1)² + 4. For every real number x, (x - 1)² is at least zero, so the expression is at least 4 and can never equal zero. Therefore, the equation has no real solution, and the set of its real solutions is empty: 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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