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NDA 2016 Maths · Mathematics · Quadratic Equations · medium

One root of x^2+px+6=0 is 3. If the equation x^2+px+q=0 has equal roots, then q is equal to

Single correct option

One root of x2+px+6=0x^2+px+6=0 is 33. If the equation x2+px+q=0x^2+px+q=0 has equal roots, then qq is equal to
  1. A. 52\dfrac52
  2. B. 66
  3. C. 2525
  4. D. 254\dfrac{25}{4}
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Answer: (D) 254\dfrac{25}{4}

Substituting x=3x=3: 9+3p+6=09+3p+6=0 gives p=−5p=-5. For equal roots of x2−5x+q=0x^2-5x+q=0 we need 25−4q=025-4q=0, so q=254q=\dfrac{25}4. Taking q=6q=6 keeps the first equation, and q=25q=25 forgets the factor 44 in the discriminant.
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Original question written in the NDA 2016 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