If U = R and A = {x ∈ R : x² + x − 6 ≥ 0}, what is A'?
Answer and explanation
Correct answer: (-3, 2)
Factor the quadratic: x² + x − 6 = (x + 3)(x − 2). Since the parabola opens upward, the expression is nonnegative outside the roots, so A = (−∞, −3] ∪ [2, ∞). The complement in R consists of the numbers strictly between the roots. The endpoints −3 and 2 belong to A because equality is allowed, so they are excluded from A'. Therefore A' = (−3, 2), option A.
Frequently asked questions
What is the correct answer to this question?
(-3, 2)
Why is this the correct answer?
Factor the quadratic: x² + x − 6 = (x + 3)(x − 2). Since the parabola opens upward, the expression is nonnegative outside the roots, so A = (−∞, −3] ∪ [2, ∞). The complement in R consists of the numbers strictly between the roots. The endpoints −3 and 2 belong to A because equality is allowed, so they are excluded from A'. Therefore A' = (−3, 2), 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.
