All the values of `m` for whilch both the roots of the equation `x^2-2m x+m^2-1=0` are greater than -2 but less than 4 lie in the interval `-23` c. `-1

Options

A. `-2 lt m lt 0 `
B. `m gt 3`
C. `- 1 lt m lt 3`
D. `1 lt m lt 4`

Answer

3

Explanation

The given equation is
`x^(3) - 2mx +m^(2) - 1 = 0 `
or `(x - m + 1) (x - m - 1) = 0 `
or ` x = m - 1 , m + 1`
From given condition,
` m - 1 gt - 2 and m+ 1 lt 4`
`rArr m gt - 1 and m lt 3`
Hence, ` - 1 lt m lt 3` .