Choose the correct statement for the set A = {x ∈ ℤ : x² − 5x + 6 = 0}.
Answer and explanation
Correct answer: A = {2, 3}; A is finite.
Factor the quadratic equation: x² − 5x + 6 = (x − 2)(x − 3) = 0. Therefore, x = 2 or x = 3. Since both values are integers, both belong to A, so A = {2, 3}. This set has exactly two distinct elements, and every set with a fixed, countable number of elements is finite. Hence option A is correct. The value 6 is the constant term, not a solution of the equation.
Frequently asked questions
What is the correct answer to this question?
A = {2, 3}; A is finite.
Why is this the correct answer?
Factor the quadratic equation: x² − 5x + 6 = (x − 2)(x − 3) = 0. Therefore, x = 2 or x = 3. Since both values are integers, both belong to A, so A = {2, 3}. This set has exactly two distinct elements, and every set with a fixed, countable number of elements is finite. Hence option A is correct. The value 6 is the constant term, not a solution of the equation.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
