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NDA 2023 Maths · Mathematics · Quadratic Equations · medium

If the roots of x^2-(k+2)x+9=0 are real and equal, the product of all possible values of k is

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If the roots of x2−(k+2)x+9=0x^2-(k+2)x+9=0 are real and equal, the product of all possible values of kk is
  1. A. −32-32
  2. B. 3232
  3. C. −8-8
  4. D. 44
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Answer: (A) −32-32

Equal roots need discriminant zero: (k+2)2−36=0(k+2)^2-36=0, so k+2=±6k+2=\pm6 and k=4k=4 or k=−8k=-8. Their product is 4×(−8)=−324\times(-8)=-32. A frequent mistake is to take only k=4k=4 (forgetting the negative root of 3636), or to report the sum −4-4.
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Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake