The values of p for which the difference between the roots

The values of p for which the difference between the roots of the equation x² + px + 8 = 0 is 2 , are

α + β = - p, α β = 8
Given, α - β = 2
On squaring both sides, we get
(α - β)² = 4
⇒ (α + β)² - 4αβ = 4
⇒ p² - 32 = 4
⇒ p² = 36 ⇒ p = ± 6