If T₁ = {x : x ∈ Z, x² − 2x − 8 = 0}, which is the correct roster form of T₁?
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Answer and explanation
Correct answer: T₁ = {−2, 4}
Factor the quadratic equation: x² − 2x − 8 = (x − 4)(x + 2) = 0. Hence x = 4 or x = −2. Both values belong to the integers and satisfy the defining equation. A set has no order requirement, so {−2, 4} and {4, −2} would describe the same set; among the given choices, option A is correct.
Frequently asked questions
What is the correct answer to this question?
T₁ = {−2, 4}
Why is this the correct answer?
Factor the quadratic equation: x² − 2x − 8 = (x − 4)(x + 2) = 0. Hence x = 4 or x = −2. Both values belong to the integers and satisfy the defining equation. A set has no order requirement, so {−2, 4} and {4, −2} would describe the same set; among the given choices, 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.
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