If x^{2}+mx+n is an integer for <strong>ALL</strong> integral values of x, then which of the following is/are correct? 1. m <strong>MUST BE</strong> an integer 2. n <strong>MUST BE</strong> an integer Select the correct answer using the code given below:
- A. 1 only
- B. 2 only
- C. Both 1 and 2 ✓
- D. Neither 1 nor 2
Correct Answer: C. Both 1 and 2
Explanation
Let P(x) = x^2+mx+n. For x = 0, P(0) = n, so n must be an integer. For x = 1, P(1) = 1+m+n. Since P(1) and n are both integers, 1+m must be an integer, which means m must be an integer.
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