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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2024 · Mathematics · Quadratic Equation

If x^2+m x+n is an integer for all integral values of x , then...

If x2+mx+nx^2+m x+n is an integer for all integral values of xx, then which of the following is/are correct? 1. mm must be an integer 2. nn must be an integer Select the correct answer using the code given below:

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

C. Both 1 and 2

Step-by-step solution

Let nn be an integer and n=0n=0∴x2+mx=0⇒x(x+m)=0⇒x=0,x=−m\begin{aligned} \therefore & & x^2+m x & =0 \\ \Rightarrow & & x(x+m) & =0 \\ \Rightarrow & & x & =0, x=-m \end{aligned}$SinceSincenisinteger,thereforeis integer, thereforem$ is also integer.
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