CDS 2026 (I) Elementary Mathematics, question 2

Topic: Algebra

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Q2

What is the value of kk for which (k2−5k+4)x2+(k2−3k−4)x+(k2−4k)=0(k^{2}-5k+4)x^{2}+(k^{2}-3k-4)x+(k^{2}-4k)=0 is an identity ?

  1. (a) −1-1
  2. (b) 00
  3. (c) 11
  4. (d) 44Correct answer

Solution.

Answer: (d) 44

  1. An identity in x requires all three coefficients to vanish.
  2. The constant coefficient gives k(k−4)=0k(k - 4) = 0, so k=0k = 0 or 4.
  3. At k=0k = 0 the x2x^{2} coefficient is 4; at k=4k = 4 all three coefficients are zero.