By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

NDA 1 2024 Maths, question 33

Topic: Algebra

Q33

If x2+mx+nx^{2}+mx+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 :

  1. (a) 1 only
  2. (b) 2 only
  3. (c) Both 1 and 2Correct answer
  4. (d) Neither 1 nor 2

Solution.

Answer: (c) Both 1 and 2

  1. Put x = 0: n is an integer.
  2. Put x = 1: 1 + m + n is an integer, so m is also an integer.
  3. Conversely, integer coefficients give an integer at every integer x.
  4. Thus both m and n must be integers.