Math Help - [SOLVED] How to solve this question?

1. [SOLVED] How to solve this question?

Given that the roots of the equation $x^2 + ax + (a + 2) = 0$ differ by 2, find the possible values of the constant a. Hence, find the possible values of the roots of the equation.

This is my solution:
$2\alpha + 2 = -a$____(1)
$\alpha(\alpha + 2) = a + 2$____(2)

From (1),
$\alpha = \frac{-a - 2}{2}$____(3)

Sub (3) into (2),

$(\frac{-a - 2}{2})(\frac{-a - 2}{2} + 2) = a + 2$
$(-a - 2)^2 + 2(-a - 2) - 8 = 0$
$a^2 + 4a + 4 - 2a - 4 -8 = 0$
$a^2 + 2a - 8 = 0$
$(a + 4)(a - 2) = 0$

Hence, I got the answer a = -4 or a = 2 but in the book the answers are a = 6 or a = -2. Where have I gone wrong?

2. Hey...I've just found out the problem and solved it. Sorry if this question troubled your inks.