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If the difference between the roots of the equation `x^2+""a x""+""1""=""0` is less than `sqrt(5)` , then the set of possible values of a is (1) `(-3,""3)` (2) `(-3,oo)` (3) `(3,oo)` (4) `(-oo,-3)`

A

`(-3,3)`

B

`(-3,oo)`

C

`(3,oo)`

D

`(-oo,-3)`

Text Solution

AI Generated Solution

To solve the problem, we need to find the set of possible values of \( a \) such that 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 of the quadratic equation**: The roots of the equation \( x^2 + ax + 1 = 0 \) can be found using the quadratic formula: \[ \alpha, \beta = \frac{-b \pm \sqrt{D}}{2a} ...
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