If the difference between the roots of the equation `x^(2)+ax+1=0` is less than `sqrt(5)`, the set of possible values of `a` is

Options

A. `(3, oo)`
B. `(-oo, -3)`
C. `(-3, 3)`
D. `(-3, oo)`

Answer

C

Explanation

Let `alpha, beta` be the roots of the equatio `x^(2) + ax + 1 = 0`. Then, `alpha + beta = - a and alpha beta = 1`.
It is given that `|alpha-beta|lt sqrt(5)`
`rArr" "(alpha-beta)^(2) lt 5`
`rArr" "(alpha+beta)^(2) - 4 alpha beta lt 5`
`rArr" "a^(2) - 4 lt 5 rArr a^(2) - 9 lt 0 rArr - 3 lt a lt 3`