If K={x:x∈Z, x³=x}, which set is K?
Answer and explanation
Correct answer: K={-1,0,1}
The defining equation is x³=x. Bring all terms to one side and factor: x³−x=x(x²−1)=x(x−1)(x+1)=0. The zero-product property gives x=0, x=1, or x=−1. All three are integers, so they satisfy the domain restriction and belong to K. Thus option A is correct; each other option omits at least one valid solution.
Frequently asked questions
What is the correct answer to this question?
K={-1,0,1}
Why is this the correct answer?
The defining equation is x³=x. Bring all terms to one side and factor: x³−x=x(x²−1)=x(x−1)(x+1)=0. The zero-product property gives x=0, x=1, or x=−1. All three are integers, so they satisfy the domain restriction and belong to K. Thus option A is correct; each other option omits at least one valid solution.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
