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

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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

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