If A = {x : x ∈ ℤ and x² − 4x + 3 = 0}, which is the correct roster form of A?
Answer and explanation
Correct answer: A = {1, 3}
To convert the set-builder form into roster form, first solve the condition given for x. Factor the quadratic as x² − 4x + 3 = (x − 1)(x − 3) = 0. Therefore, x = 1 or x = 3. Both values are integers, so both belong to A. Hence, the elements listed in roster form are A = {1, 3}. The order of elements is not important in a set.
Frequently asked questions
What is the correct answer to this question?
A = {1, 3}
Why is this the correct answer?
To convert the set-builder form into roster form, first solve the condition given for x. Factor the quadratic as x² − 4x + 3 = (x − 1)(x − 3) = 0. Therefore, x = 1 or x = 3. Both values are integers, so both belong to A. Hence, the elements listed in roster form are A = {1, 3}. The order of elements is not important in a set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
