How many elements are in A = {x ∈ ℝ : x² − 4x + 4 = 0}?
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Answer and explanation
Correct answer: 1
Factor the expression as x² − 4x + 4 = (x − 2)². The equation is zero only when x − 2 = 0, so x = 2. Consequently, A = {2} and has exactly one element. Although 2 is a repeated root of the polynomial, a set lists an element only once; repeated occurrence does not increase the cardinality.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
Factor the expression as x² − 4x + 4 = (x − 2)². The equation is zero only when x − 2 = 0, so x = 2. Consequently, A = {2} and has exactly one element. Although 2 is a repeated root of the polynomial, a set lists an element only once; repeated occurrence does not increase the cardinality.
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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