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Find the zeroes of the quadratic polynomial f(x) = 4√3x2 + 5x – 2√3.

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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 \(\frac{\sqrt3}{4}\)

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