If A = {x ∈ R : x² - 2x + 2 = 0}, what is A?
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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 0, so (x - 1)² + 1 is at least 1 and can never equal 0. Therefore, the equation has no real solution, and the set of real solutions is empty. Hence option A is correct.
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 0, so (x - 1)² + 1 is at least 1 and can never equal 0. Therefore, the equation has no real solution, and the set of real solutions is empty. Hence option A is correct.
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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