If G = {x ∈ Z : x² < 2x + 8}, which is the correct roster form of G?
Advertisement
Answer and explanation
Correct answer: G = {-1, 0, 1, 2, 3}
Rearrange the inequality: x² − 2x − 8 < 0. Factoring gives (x − 4)(x + 2) < 0, which holds strictly when −2 < x < 4. Since x must be an integer, the possible values are −1, 0, 1, 2, and 3. The endpoints −2 and 4 give equality, not a strict inequality, so they are excluded. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
G = {-1, 0, 1, 2, 3}
Why is this the correct answer?
Rearrange the inequality: x² − 2x − 8 < 0. Factoring gives (x − 4)(x + 2) < 0, which holds strictly when −2 < x < 4. Since x must be an integer, the possible values are −1, 0, 1, 2, and 3. The endpoints −2 and 4 give equality, not a strict inequality, so they are excluded. Thus option 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.
Advertisement