What is the roster form of D = {x : x ∈ N and x² - 5x + 6 = 0}?
Answer and explanation
Correct answer: D = {2, 3}
Solve the defining equation before applying the set restriction. Factorisation gives x² − 5x + 6 = (x − 2)(x − 3) = 0, so x = 2 or x = 3. Both roots are natural numbers, hence both belong to D and D = {2, 3}. The negative values are not roots of this factorisation, 1 and 6 do not make the expression zero, and 0 is not a solution either.
Frequently asked questions
What is the correct answer to this question?
D = {2, 3}
Why is this the correct answer?
Solve the defining equation before applying the set restriction. Factorisation gives x² − 5x + 6 = (x − 2)(x − 3) = 0, so x = 2 or x = 3. Both roots are natural numbers, hence both belong to D and D = {2, 3}. The negative values are not roots of this factorisation, 1 and 6 do not make the expression zero, and 0 is not a solution either.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: General chapter practice.
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