If Z₁ = {x : x ∈ ℕ and x² + x = 20}, what is the correct roster form of Z₁?
Answer and explanation
Correct answer: Z₁ = {4} — Z₁ = {4}
Start with x² + x = 20 and bring all terms to one side: x² + x − 20 = 0. Factoring gives (x + 5)(x − 4) = 0, so the algebraic solutions are x = −5 and x = 4. However, the set specifies x ∈ ℕ, and −5 is not a natural number. Only 4 satisfies both the equation and the domain condition, so Z₁ = {4}. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
Z₁ = {4} — Z₁ = {4}
Why is this the correct answer?
Start with x² + x = 20 and bring all terms to one side: x² + x − 20 = 0. Factoring gives (x + 5)(x − 4) = 0, so the algebraic solutions are x = −5 and x = 4. However, the set specifies x ∈ ℕ, and −5 is not a natural number. Only 4 satisfies both the equation and the domain condition, so Z₁ = {4}. 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.
