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Subjects
Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsMediumLevel 4

If A = {x ∈ ℝ : x² = x + 2} and B = {-1, 2}, choose the correct option.

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Answer and explanation

Correct answer: A = B

Rearrange the equation as x² - x - 2 = 0. Factoring gives (x - 2)(x + 1) = 0, so x = 2 or x = -1. Both values are real and therefore A = {-1, 2}. Since B contains exactly these same elements, A = B. The order in which elements are written does not affect a set.

Tags

setsequal setssolution setquadratic equationThe Empty SetFinite and Infinite Setsthe empty set finite and infinite sets equal setsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

A = B

Why is this the correct answer?

Rearrange the equation as x² - x - 2 = 0. Factoring gives (x - 2)(x + 1) = 0, so x = 2 or x = -1. Both values are real and therefore A = {-1, 2}. Since B contains exactly these same elements, A = B. The order in which elements are written does not affect a set.

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.

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