Correct Answer - Option 2 :
± 6
Concept:
If α and β are the roots of the quadratic equation ax2 + bx + c = 0,then α + β = -b/a, αβ = c/a.
Calculation:
Given quadratic equation x2 - px + 5 = 0
Let α and β be the roots of the equation x2 - px + 5 = 0
As we know that if roots of quadratic equation ax2 + bx + c = 0 are α and β,then α + β = - b/a, αβ = c/a
⇒ α + β = p, αβ = 5.
It is given that |α - β| = 4.
(α + β)2 = (α - β)2 + 4αβ
⇒ (p)2 = (4)2 + 4 ⋅ 5 = 16 + 20
⇒ p2 = 36 ⇒ p = ± 6
Hence, option 2 is correct.