If A = {x ∈ R | x² − 5x + 6 = 0} and B = {x ∈ R | x² − 4x + 3 = 0}, what is A ∩ B?
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Answer and explanation
Correct answer: {3}
Factor the first quadratic: x² − 5x + 6 = (x − 2)(x − 3), so A = {2, 3}. Factor the second: x² − 4x + 3 = (x − 1)(x − 3), so B = {1, 3}. The intersection contains only values present in both sets. The only common value is 3, hence A ∩ B = {3}. Option A is correct.
Frequently asked questions
What is the correct answer to this question?
{3}
Why is this the correct answer?
Factor the first quadratic: x² − 5x + 6 = (x − 2)(x − 3), so A = {2, 3}. Factor the second: x² − 4x + 3 = (x − 1)(x − 3), so B = {1, 3}. The intersection contains only values present in both sets. The only common value is 3, hence A ∩ B = {3}. Option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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