If Y = {x ∈ N : x² + x = 12}, which set is Y?
Answer and explanation
Correct answer: English: Y = {3} | हिन्दी: Y = {3}
Rewrite the equation as x² + x − 12 = 0. Factoring gives (x + 4)(x − 3) = 0, so the algebraic solutions are x = −4 and x = 3. However, the set is restricted to natural numbers. Under the usual school convention, −4 is not a natural number, whereas 3 is natural. Consequently only 3 belongs to Y, and the required set is Y = {3}. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
English: Y = {3} | हिन्दी: Y = {3}
Why is this the correct answer?
Rewrite the equation as x² + x − 12 = 0. Factoring gives (x + 4)(x − 3) = 0, so the algebraic solutions are x = −4 and x = 3. However, the set is restricted to natural numbers. Under the usual school convention, −4 is not a natural number, whereas 3 is natural. Consequently only 3 belongs to Y, and the required set is Y = {3}. Therefore option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
