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NDA 2020 Maths · Mathematics · Quadratic Equations · medium

The equation x^2-(m-2)x+(m+1)=0 has equal roots for two values of m. Their sum is

Single correct option

The equation x2−(m−2)x+(m+1)=0x^2-(m-2)x+(m+1)=0 has equal roots for two values of mm. Their sum is
  1. A. 8
  2. B. 4
  3. C. 0
  4. D. −8-8
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Answer: (A) 8

Equal roots need (m−2)2=4(m+1)(m-2)^2=4(m+1), i.e. m2−4m+4=4m+4m^2-4m+4=4m+4, so m2−8m=0m^2-8m=0. The roots are m=0m=0 and m=8m=8, whose sum is 8. The product, 0, is a different quantity, and 4 comes from halving.
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Original question written in the NDA 2020 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