Which is the roster form of U = {x : x ∈ ℤ and x² − 5x + 6 = 0}?
Answer and explanation
Correct answer: U = {2, 3}
To find the members of U, solve the defining equation. We factor x² − 5x + 6 as (x − 2)(x − 3). Hence, the product is zero when x = 2 or x = 3. Both values are integers, so both belong to the set. There are no other roots of this quadratic equation. Thus the roster form is U = {2, 3}, making option A correct.
Frequently asked questions
What is the correct answer to this question?
U = {2, 3}
Why is this the correct answer?
To find the members of U, solve the defining equation. We factor x² − 5x + 6 as (x − 2)(x − 3). Hence, the product is zero when x = 2 or x = 3. Both values are integers, so both belong to the set. There are no other roots of this quadratic equation. Thus the roster form is U = {2, 3}, making option A correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
