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JEE Main 2021 · Mathematics · Quadratic Equations · medium

The number of integer values of m for which both roots of x^2-2mx+m^2-1=0 lie strictly between -2 and 4 is

Single correct option

The number of integer values of mm for which both roots of x2−2mx+m2−1=0x^2-2mx+m^2-1=0 lie strictly between −2-2 and 44 is
  1. A. 22
  2. B. 44
  3. C. 33
  4. D. 55
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Answer: (C) 33

The discriminant is 4m2−4(m2−1)=44m^2-4(m^2-1)=4, and the equation factors as (x−m)2=1(x-m)^2=1, so the roots are m−1m-1 and m+1m+1. Both lie in (−2,4)(-2,4) exactly when m−1>−2m-1>-2 and m+1<4m+1<4, that is −1<m<3-1<m<3. The integers are m=0,1,2m=0,1,2, so there are 33 values. Including the end values m=−1,3m=-1,3 (roots touching −2-2 or 44) would wrongly give 55.
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