If D = {x : x ∈ Z, x² + x − 6 = 0}, what is the correct roster form of D?
Answer and explanation
Correct answer: D = {-3, 2}
The governing concept is roster representation using the integer solutions of the defining equation. Factor the quadratic: x² + x − 6 = (x + 3)(x − 2). Therefore (x + 3)(x − 2) = 0 gives x = −3 or x = 2. Both values belong to the integers, so D = {−3, 2}. The other options arise from incorrect signs or from using roots that do not satisfy the equation. Hence A is correct.
Frequently asked questions
What is the correct answer to this question?
D = {-3, 2}
Why is this the correct answer?
The governing concept is roster representation using the integer solutions of the defining equation. Factor the quadratic: x² + x − 6 = (x + 3)(x − 2). Therefore (x + 3)(x − 2) = 0 gives x = −3 or x = 2. Both values belong to the integers, so D = {−3, 2}. The other options arise from incorrect signs or from using roots that do not satisfy the equation. Hence A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
