Over the real numbers, what type of set is {x : x ∈ R, x² + 1 = 0}?
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Answer and explanation
Correct answer: Empty set
For every real number x, x² is nonnegative, so x² + 1 is at least 1 and can never equal zero. Alternatively, the equation would give x² = −1, which has no real solution; its solutions are imaginary numbers. Because the domain is R, no solution is admitted, and the set is empty.
Frequently asked questions
What is the correct answer to this question?
Empty set
Why is this the correct answer?
For every real number x, x² is nonnegative, so x² + 1 is at least 1 and can never equal zero. Alternatively, the equation would give x² = −1, which has no real solution; its solutions are imaginary numbers. Because the domain is R, no solution is admitted, and the set is empty.
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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