Let `alpha and beta (a lt beta) " be the roots of the equation " x^(2) + bx + c = 0," where " b gt 0 and c lt 0 . `
If both the roots of the equation `x^(2) - 2 kx + k^(2) - 4 = 0 ` lie between` -3 and 5`, then which one of the following is correct ?

Options

A. `-2 lt k lt 2.`
B. `-5lt k lt3`
C. ` -3 lt k lt 5`
D. ` -1 lt k lt 3`

Answer

D

Explanation

` x^(2) - 2 kx + k^(2) - 4 = 0 `
`rArr (x-k)^(2) - 2^(2) = 0 `
` rArr (x- k - 2) ( x- k+ 2) = 0 `
` rArr x= k + 2, k-2.`
`rArr k+2 lt 5 & k-2 gt -3`
`rArr k lt 3 & k gt -1`
` rArr -1 lt k lt 3 `