Find the values of k ε R subject to the following condition :

The diffrenence between the roots of $x^2 + kx + 4 = 0 is 3.$

** Option:**

**A.**5

**B.**± 5

**C.**0

**D.**8

**Answer: B . ± 5**

** Justification:**

Here, If the roots of the equation are α and β (α > β), then α - β = 3

Also, α + β = -k and αβ = $4/1 = 4$

Now, $ (α+ β)^2 = (α - β)^2 + 4αβ$

.`. $k^2 = 9 + 4(4)$

.`. $k^2 = 25$

.`. k = ±5