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Which is the roster form of B₃ = {x ∈ ℤ : x² − 5x + 6 = 0}?
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Answer and explanation
Correct answer: {2, 3}
To find the members of B₃, solve the quadratic equation x² − 5x + 6 = 0. Factoring gives (x − 2)(x − 3) = 0. Hence x = 2 or x = 3. Both values are integers and satisfy the original equation, so the set contains exactly these two elements. Its roster form is {2, 3}.
Frequently asked questions
What is the correct answer to this question?
{2, 3}
Why is this the correct answer?
To find the members of B₃, solve the quadratic equation x² − 5x + 6 = 0. Factoring gives (x − 2)(x − 3) = 0. Hence x = 2 or x = 3. Both values are integers and satisfy the original equation, so the set contains exactly these two elements. Its roster form is {2, 3}.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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