If E={x:x∈Z, x²-5x+6=0}, what is E?
Answer and explanation
Correct answer: E={2,3}
Solve the defining equation by factoring: x²−5x+6=(x−2)(x−3). A product is zero when at least one factor is zero, so x−2=0 or x−3=0. Hence x=2 or x=3; both are integers and satisfy the original equation. Therefore E={2,3}, making option A correct. The other options contain incorrect or extra roots.
Frequently asked questions
What is the correct answer to this question?
E={2,3}
Why is this the correct answer?
Solve the defining equation by factoring: x²−5x+6=(x−2)(x−3). A product is zero when at least one factor is zero, so x−2=0 or x−3=0. Hence x=2 or x=3; both are integers and satisfy the original equation. Therefore E={2,3}, making option A correct. The other options contain incorrect or extra roots.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: General chapter practice.
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