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NDA 2 2025 Maths, question 32

Topic: Algebra

Passage · Q31 to Q32

Consider the equation

abx2+bcx+ca=cax2+abx+bcabx^{2}+bcx+ca=cax^{2}+abx+bc

Q32

If the roots of the equation are equal, then a,b,ca,b,c are in

  1. (a) AP
  2. (b) GP
  3. (c) HPCorrect answer
  4. (d) None of the above

Solution.

Answer: (c) HP

  1. The equal-root condition from the polynomial is 1/a+1/c=2/b.
  2. Therefore 1/a,1/b,1/c form an AP, which means a,b,c form an HP.
  3. This concerns a nondegenerate quadratic with two roots, as stated.