If the roots of `x^2 - 2mx + m^2 - 1=0` lie between `-2and 4,then`

Options

A. `-1 le m le 3`
B. `-3 le m le 3`
C. `-3 le m le 5`
D. ` -1 le m le 5`

Answer

B

Explanation

Since the roots of `x^(2) - 2 mx + m^(2) = 0 " lie between" `
` -2 and 4 i.e., b^(2) - 4ac ge 0 and -2 lt (-b)/(2a) lt 4 `
` :. (2m)^(2) - 4(m^(2)-1) ge 0 " "` ...(1)
and `-2 lt (2m)/2 lt 4 `
`rArr -2 ltm lt 4 `
From (i)
` 4m^(2) - 4m^(2) + 4 ge0`
`rArr m in R`
and `f(-2) gt 0, " also f "(4) gt 0.`
`4+ 4m + m^(2) - 1 gt 0, 16- 8m + m^(2) - 1 gt0`
` rArr m^(2) + 4m + 3 gt 0, m^(2) - 8m + 15 gt 0`
`rArr (m+1) (m+3) gt 0, (m-3) (m-5) gt 0,`
`rArr -3 lt m lt -1 and 3 lt m lt 5.`