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If F = {x ∈ Z : x² < 2x + 8}, what is F?
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Answer and explanation
Correct answer: F = {-2, -1, 0, 1, 2, 3}
Rearrange the inequality: x² − 2x − 8 < 0. Factoring gives (x − 4)(x + 2) < 0, which holds for −2 < x < 4. The integer values in this open interval are −1, 0, 1, 2, and 3. Therefore, none of the original options was correct; option A is corrected here to the actual set.
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What is the correct answer to this question?
F = {-2, -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 for −2 < x < 4. The integer values in this open interval are −1, 0, 1, 2, and 3. Therefore, none of the original options was correct; option A is corrected here to the actual set.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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