Which statement is correct about the set I = {x : x ∈ ℝ, x² + 1 = 0}?
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Answer and explanation
Correct answer: I = ∅
For every real number x, x² is non-negative, so x² ≥ 0. Consequently, x² + 1 ≥ 1, which means that x² + 1 can never equal zero when x is real. The equation would have complex solutions x = i and x = −i, but those are not real numbers. Hence the set of real solutions is empty: I = ∅.
Frequently asked questions
What is the correct answer to this question?
I = ∅
Why is this the correct answer?
For every real number x, x² is non-negative, so x² ≥ 0. Consequently, x² + 1 ≥ 1, which means that x² + 1 can never equal zero when x is real. The equation would have complex solutions x = i and x = −i, but those are not real numbers. Hence the set of real solutions is empty: I = ∅.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
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