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NDA 1 2025 Maths, question 3

Topic: Algebra

Q3

If one root of the equation x2−kx+k=0x^{2} - kx + k = 0 exceeds the other by 232\sqrt{3}, then which one of the following is a value of kk?

  1. (a) 3
  2. (b) 6Correct answer
  3. (c) 9
  4. (d) 12

Solution.

Answer: (b) 6

  1. For roots α,β\alpha,\beta, α+β=k\alpha + \beta = k and αβ=k\alpha\beta = k.
  2. Thus (α−β)2=k2−4k=12(\alpha - \beta)^{2} = k^{2} - 4k = 12.
  3. Solving k2−4k−12=(k−6)(k+2)=0k^{2} - 4k - 12 = (k - 6)(k + 2) = 0 gives k=6k = 6 or −2- 2.
  4. Only 6 is listed.