If A = {x : x ∈ ℕ and x² − 7x + 10 = 0}, what is the roster form of A?
Advertisement
Answer and explanation
Correct answer: A = {2, 5}
Factor the quadratic expression: x² − 7x + 10 = (x − 2)(x − 5). Setting each factor equal to zero gives x = 2 or x = 5. Both values are natural numbers and satisfy the original equation: 4 − 14 + 10 = 0 and 25 − 35 + 10 = 0. Therefore, the roster form is A = {2, 5}.
Frequently asked questions
What is the correct answer to this question?
A = {2, 5}
Why is this the correct answer?
Factor the quadratic expression: x² − 7x + 10 = (x − 2)(x − 5). Setting each factor equal to zero gives x = 2 or x = 5. Both values are natural numbers and satisfy the original equation: 4 − 14 + 10 = 0 and 25 − 35 + 10 = 0. Therefore, the roster form is A = {2, 5}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
Advertisement