2x2 + 5√3 x + 16 = 0

(vi) 2x² + 5√3 x + 16 = 0

Sol. 2x² + 5√3 x + 16 = 0

Comparing with ax² + bx + c = 0 we have a = 2, b = 5 3 , c = 16

∴ ∆  = b² – 4ac

= (5√3 )² – 4 (2) (16)

= 25 × 3 – 128

= 75 – 128

= – 53

∴ ∆  < 0

Hence roots of the quadratic equation are not real.