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NDA 2 2024 Maths, question 16

Topic: Algebra

Q16

If nn is a root of the equation x2+px+m=0x^{2}+px+m=0 and mm is a root of the equation x2+px+n=0x^{2}+px+n=0, where m≠nm\ne n, then what is the value of p+m+np+m+n?

  1. (a) −1-1
  2. (b) 00
  3. (c) 11Correct answer
  4. (d) 22

Solution.

Answer: (c) 11

  1. Substitute the stated roots: n²+pn+m=0 and m²+pm+n=0.
  2. Subtraction gives (n−m)(n+m+p−1)=0.
  3. As n≠m, p+m+n=1.