If the difference between the roots of the equation `x^2+a x+1=0` is less then `sqrt(5)` , then find the set of possible value of `adot`

Options

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

Explanation

To solve the problem, we need to find the set of possible values of \( a \) for which the difference between the roots of the quadratic equation \( x^2 + ax + 1 = 0 \) is less than \( \sqrt{5} \).

### Step-by-Step Solution:

1. **Identify the Roots**:
The roots of the quadratic equation \( x^2 + ax + 1 = 0 \) can be found using the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
...