If J={x:x∈N, x²-10x+21=0}, which is its roster form?
Answer and explanation
Correct answer: J={3,7}
Use factorisation to solve the condition defining the set: x²−10x+21=(x−3)(x−7)=0. Hence x=3 or x=7. Both values are natural numbers, so both belong to J, and there are no other roots. Therefore the roster form is {3,7}, making option A correct. Negative numbers are outside the given domain, while 21 is only the product of the roots.
Frequently asked questions
What is the correct answer to this question?
J={3,7}
Why is this the correct answer?
Use factorisation to solve the condition defining the set: x²−10x+21=(x−3)(x−7)=0. Hence x=3 or x=7. Both values are natural numbers, so both belong to J, and there are no other roots. Therefore the roster form is {3,7}, making option A correct. Negative numbers are outside the given domain, while 21 is only the product of the roots.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems.
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