Which option correctly represents N₁ = {x : x ∈ Z, x² + x = 0}?
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Answer and explanation
Correct answer: N₁ = {−1, 0}
Factor the equation as x² + x = x(x + 1) = 0. By the zero-product property, either x = 0 or x + 1 = 0, which gives x = −1. Both solutions are integers, as required by the definition of the set. Therefore, N₁ contains exactly −1 and 0, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
N₁ = {−1, 0}
Why is this the correct answer?
Factor the equation as x² + x = x(x + 1) = 0. By the zero-product property, either x = 0 or x + 1 = 0, which gives x = −1. Both solutions are integers, as required by the definition of the set. Therefore, N₁ contains exactly −1 and 0, so option B is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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