If P₁ = {x : x ∈ ℕ and x² − 10x + 21 = 0}, which is P₁?
Answer and explanation
Correct answer: P₁ = {3, 7}
To find the members of P₁, solve the condition x² − 10x + 21 = 0. Factoring gives (x − 3)(x − 7) = 0, so x = 3 or x = 7. Both values are natural numbers, so both belong to the set. The roster form is therefore {3, 7}. Negative values are not roots of this equation, 1 and 21 are not solutions, and 0 is not a solution.
Frequently asked questions
What is the correct answer to this question?
P₁ = {3, 7}
Why is this the correct answer?
To find the members of P₁, solve the condition x² − 10x + 21 = 0. Factoring gives (x − 3)(x − 7) = 0, so x = 3 or x = 7. Both values are natural numbers, so both belong to the set. The roster form is therefore {3, 7}. Negative values are not roots of this equation, 1 and 21 are not solutions, and 0 is not a solution.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
