Q183 / 270 · NDA 2024 (Phase 1) · Mathematics

If $x^2+m x+n$ is an integer for all integral values of $x$, then which of the following is/are correct? 1. $m$ must be an integer 2. $n$ must be an integer Select the correct answer using the code given below:

  • A
    1 only
  • B
    2 only
  • Correct answer
    C
    Both 1 and 2
  • D
    Neither 1 nor 2

Solution

Let $n$ be an integer and $n=0$ $\begin{aligned} \therefore & & x^2+m x & =0 \\ \Rightarrow & & x(x+m) & =0 \\ \Rightarrow & & x & =0, x=-m \end{aligned}$ Since $n$ is integer, therefore $m$ is also integer.

Hence, the correct answer is option: 'C'.

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