If U = R and A = {x : x² − 4x − 12 < 0}, what is A'?
Advertisement
Answer and explanation
Correct answer: (-∞, -2] ∪ [6, ∞)
Factor the quadratic: x² − 4x − 12 = (x − 6)(x + 2). Because the parabola opens upward, the expression is negative between its roots, so A = (-2, 6). The complement in R contains the endpoints and the two outside intervals. Therefore, A' = (-∞, -2] ∪ [6, ∞), which is option A.
Frequently asked questions
What is the correct answer to this question?
(-∞, -2] ∪ [6, ∞)
Why is this the correct answer?
Factor the quadratic: x² − 4x − 12 = (x − 6)(x + 2). Because the parabola opens upward, the expression is negative between its roots, so A = (-2, 6). The complement in R contains the endpoints and the two outside intervals. Therefore, A' = (-∞, -2] ∪ [6, ∞), which is option A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
Advertisement