To find the zeroes of the quadratic polynomial we will equate f(x) to 0
∴f(x) = 0
⇒ 4√3x2 + 5x – 2√3 = 0
⇒ 4√3x2 + 8x – 3x – 2√3 = 0
⇒ 4x (√3x + 2) – √3(√3x + 2) = 0
⇒ (√3x + 2) = 0 or (4x – √3) = 0
⇒ x = – \(\frac{2}{\sqrt3}\) or x = \(\frac{\sqrt3}{4}\)
Hence, the zeroes of the quadratic polynomial f(x) = 4√3x2 + 5x – 2√3 are – \(\frac{2}{\sqrt3}\) or \(\frac{\sqrt3}{4}\)