If T = {x ∈ ℕ : x² − 5x + 6 = 0}, what is T?
Answer and explanation
Correct answer: T = {2, 3}
To find the members of T, solve the condition x² − 5x + 6 = 0. Factoring gives (x − 2)(x − 3) = 0, so x = 2 or x = 3. Both values are natural numbers, so both satisfy the restriction x ∈ ℕ. Therefore, the set contains exactly these two elements: T = {2, 3}. Thus option A is correct; the other options either contain incorrect roots or include numbers that are not solutions.
Frequently asked questions
What is the correct answer to this question?
T = {2, 3}
Why is this the correct answer?
To find the members of T, solve the condition x² − 5x + 6 = 0. Factoring gives (x − 2)(x − 3) = 0, so x = 2 or x = 3. Both values are natural numbers, so both satisfy the restriction x ∈ ℕ. Therefore, the set contains exactly these two elements: T = {2, 3}. Thus option A is correct; the other options either contain incorrect roots or include numbers that are not solutions.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
