If A = {x ∈ Z : x² − 6x + 9 = 0} and B = {3, 3, 3}, choose the correct statement.
Answer and explanation
Correct answer: A = B, because both sets contain only the element 3
The quadratic x² − 6x + 9 is (x − 3)², so its only integer solution is x = 3. Thus A = {3}. In set notation, repetitions do not create additional elements; writing 3 three times still represents B = {3}. Consequently A and B contain exactly the same element and are equal. Repeated roots affect multiplicity in algebra, but not the number of distinct elements in a set.
Frequently asked questions
What is the correct answer to this question?
A = B, because both sets contain only the element 3
Why is this the correct answer?
The quadratic x² − 6x + 9 is (x − 3)², so its only integer solution is x = 3. Thus A = {3}. In set notation, repetitions do not create additional elements; writing 3 three times still represents B = {3}. Consequently A and B contain exactly the same element and are equal. Repeated roots affect multiplicity in algebra, but not the number of distinct elements in a set.
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.
