All the value of m for which both the roots of the equation x 2 −2mx+m 2 −1=0 are greater than −2 but less than 4 lie in the interval a -23` c. `-1

Options

A. `-2ltmlt0`
B. `mgt3`
C. `-1ltmlt3`
D. `1ltmlt4`

Answer

C

Explanation

`:'x^(2)-2mx+m^(2)-1=0`
`implies(x-m)^(2)=1`
`:.x-m=+-1` or `x=m-1,m+1`
According to the question
`m-1gt-2,m+1gt-2`
`impliesmgt-1,mgt-3`
Then `mgt-1`…………I
and `m-1lt4,mm+1lt4`
`impliesmlt5,mlt3` and `mlt3`
From Eqs I and ii we get `-1ltmlt3`