If A = {x ∈ ℕ : x² − 5x + 6 = 0}, which set is equal to A?
Answer and explanation
Correct answer: {2, 3}
Find the natural-number solutions by factoring the quadratic: x² − 5x + 6 = (x − 2)(x − 3). Hence x = 2 or x = 3. Both values are natural numbers, so the set defined by the condition is A = {2, 3}. Therefore, option B is equal to A. Option A uses incorrect roots, option C gives unrelated negative values, and option D wrongly treats the solution set as empty.
Frequently asked questions
What is the correct answer to this question?
{2, 3}
Why is this the correct answer?
Find the natural-number solutions by factoring the quadratic: x² − 5x + 6 = (x − 2)(x − 3). Hence x = 2 or x = 3. Both values are natural numbers, so the set defined by the condition is A = {2, 3}. Therefore, option B is equal to A. Option A uses incorrect roots, option C gives unrelated negative values, and option D wrongly treats the solution set as empty.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, many more. Step 3: Hence the set is infinite..
