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Class 10MathematicsSetsSets and their representationsMediumLevel 3

If K₁ = {x : x ∈ N, x² − 5x + 6 ≤ 0}, what is the roster form of K₁?

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Answer and explanation

Correct answer: K₁ = {2, 3}

Factor the quadratic: x² − 5x + 6 = (x − 2)(x − 3). Since the parabola opens upward, the expression is less than or equal to zero between the roots, including the endpoints. Thus 2 ≤ x ≤ 3. The natural numbers in this interval are only 2 and 3, so the roster form is K₁ = {2, 3}.

Tags

setsquadratic inequalityroster formnatural numbersSets and their representationsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

K₁ = {2, 3}

Why is this the correct answer?

Factor the quadratic: x² − 5x + 6 = (x − 2)(x − 3). Since the parabola opens upward, the expression is less than or equal to zero between the roots, including the endpoints. Thus 2 ≤ x ≤ 3. The natural numbers in this interval are only 2 and 3, so the roster form is K₁ = {2, 3}.

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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