Which statement is correct about A = {x ∈ ℤ : x² + x + 1 = 0}?
Answer and explanation
Correct answer: A = ∅
For the quadratic equation x² + x + 1 = 0, the discriminant is b² − 4ac = 1² − 4(1)(1) = −3. Since the discriminant is negative, the equation has no real roots. Every integer is a real number, so it cannot have any integer solution either. Therefore, no element satisfies the defining condition, and A is the empty set, written as ∅.
Frequently asked questions
What is the correct answer to this question?
A = ∅
Why is this the correct answer?
For the quadratic equation x² + x + 1 = 0, the discriminant is b² − 4ac = 1² − 4(1)(1) = −3. Since the discriminant is negative, the equation has no real roots. Every integer is a real number, so it cannot have any integer solution either. Therefore, no element satisfies the defining condition, and A is the empty set, written as ∅.
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.
