Which is the correct roster form of S={x:x∈Z, x²=9}?
Answer and explanation
Correct answer: S={-3,3}
Solving x²=9 over the integers requires considering both square roots of 9. Since 3²=9 and (-3)²=9, the integer solutions are x=3 and x=-3. A set lists both distinct solutions, so S={-3,3}. Option A and option B each omit one valid solution, while option D contains values that do not all satisfy the equation. Therefore C is correct.
Frequently asked questions
What is the correct answer to this question?
S={-3,3}
Why is this the correct answer?
Solving x²=9 over the integers requires considering both square roots of 9. Since 3²=9 and (-3)²=9, the integer solutions are x=3 and x=-3. A set lists both distinct solutions, so S={-3,3}. Option A and option B each omit one valid solution, while option D contains values that do not all satisfy the equation. Therefore C is correct.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Rational numbers.
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