The set {x ∈ ℝ : x² − 5x + 6 = 0} is equal to which set?
Answer and explanation
Correct answer: {2, 3}
Factor the quadratic expression: x² − 5x + 6 = (x − 2)(x − 3). Therefore, the equation is satisfied when x = 2 or x = 3. Since x is restricted to real numbers and both values are real, the solution set contains exactly these two elements. Hence the given set is {2, 3}. The order of elements does not affect a set.
Frequently asked questions
What is the correct answer to this question?
{2, 3}
Why is this the correct answer?
Factor the quadratic expression: x² − 5x + 6 = (x − 2)(x − 3). Therefore, the equation is satisfied when x = 2 or x = 3. Since x is restricted to real numbers and both values are real, the solution set contains exactly these two elements. Hence the given set is {2, 3}. The order of elements does not affect 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.
