If A = {x ∈ ℝ : x² + 2x + 1 = 0}, which set is equal to A?
Answer and explanation
Correct answer: {-1} — {-1}
Factor the quadratic expression: x² + 2x + 1 = (x + 1)². Therefore, the equation becomes (x + 1)² = 0, which has the single real solution x = −1. A set records an element only once, even when that element is a repeated root of an equation. Hence A contains exactly one element and A = {−1}. Option A is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
{-1} — {-1}
Why is this the correct answer?
Factor the quadratic expression: x² + 2x + 1 = (x + 1)². Therefore, the equation becomes (x + 1)² = 0, which has the single real solution x = −1. A set records an element only once, even when that element is a repeated root of an equation. Hence A contains exactly one element and A = {−1}. Option A is the only correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
