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Class 10MathematicsSetsSets and their representationsEasyLevel 3

If Q = {x : x ∈ ℤ, x² − 4x + 3 = 0}, what is the roster form of Q?

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Answer and explanation

Correct answer: Q = {1, 3}

Factor the quadratic expression: x² − 4x + 3 = (x − 1)(x − 3). By the zero-product property, either x − 1 = 0 or x − 3 = 0, giving x = 1 or x = 3. Both values are integers and satisfy the original equation. Therefore, the roster form of the solution set is Q = {1, 3}.

Tags

setsquadratic equationsintegersroster formSets and their representationsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

Q = {1, 3}

Why is this the correct answer?

Factor the quadratic expression: x² − 4x + 3 = (x − 1)(x − 3). By the zero-product property, either x − 1 = 0 or x − 3 = 0, giving x = 1 or x = 3. Both values are integers and satisfy the original equation. Therefore, the roster form of the solution set is Q = {1, 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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