If H₁ = {x : x ∈ ℤ and x³ = x}, what is the roster form of H₁?
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Answer and explanation
Correct answer: H₁ = {-1, 0, 1}
To find the members, solve the defining equation x³ = x. Moving all terms to one side gives x³ − x = 0, which factors as x(x² − 1) = x(x − 1)(x + 1) = 0. Hence x is −1, 0, or 1. All three values are integers and satisfy the original equation, so the roster form is option A.
Frequently asked questions
What is the correct answer to this question?
H₁ = {-1, 0, 1}
Why is this the correct answer?
To find the members, solve the defining equation x³ = x. Moving all terms to one side gives x³ − x = 0, which factors as x(x² − 1) = x(x − 1)(x + 1) = 0. Hence x is −1, 0, or 1. All three values are integers and satisfy the original equation, so the roster form is option A.
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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