(i) 4x² + 4√3x + 3 = 0

Converting the equation into a²+2ab+b² form, we get,

⇒ (2x)² + 2 × 2x × √3 + (√3)² = 0

⇒ (2x + √3)² = 0

⇒ (2x + √3) = 0 and (2x + √3) = 0

Therefore, either x = -√3/2 or x = -√3/2.

(ii) 2x² + x + 4 = 0

⇒ 2x² + x = -4

Dividing both sides of the equation by 2, we get

⇒ x² + 1/2x = 2

⇒ x² + 2 × x × 1/4 = -2

By adding (1/4)² to both sides of the equation, we get

⇒ (x)² + 2 × x × 1/4 + (1/4)² = (1/4)² – 2

⇒ (x + 1/4)² = 1/16 – 2

⇒ (x + 1/4)² = -31/16

The square of numbers cannot be negative.

Therefore, there is no real root for the given equation, 2x² + x + 4 = 0.