If both roots of the quadratic equation `x^(2)-2ax+a^(2)-1=0` lie in `(-2,2)` which one of the following ca be `[a]`? (where [.] denotes the greatest integer function)

Options

A. `-1, 0`
B. 0, 1
C. 1, 2
D. none of these

Answer

A

Explanation

We have, `x^(2) - 2ax + a^(2) - 1 = 0`
`rArr" "(x-a)^(2) - 1^(2) = 0`
`rArr" "(x-a+1)(x - a - 1) = 0 rArr x = a - 1, x = a + 1`
Thus, the roots are a -1 and a + 1. Also, `a + 1 gt a - 1`.
For these roots to lie between -1 and 1, we must have `a - 1 gt - 2 and a + 1 lt 2`
`rArr" "a gt -1 and a lt 1 rArr -1 lt a lt 1 rArr [a] = -1, 0`