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find the zeros of the polynomial √3x²-8x+4√3 and verify the relationship between the zeroes and the coefficient

$Let α and β are the roots of the equation \sqrt{3} x^{2} - 8 x + 4 \sqrt{3} = 0 \Rightarrow α + β = \frac{8}{\sqrt{3}} - - - (i) α β = 4 {(α - β)}^{2} = {(α + β)}^{2} - 4 α β \Rightarrow {(α - β)}^{2} = {(\frac{8}{\sqrt{3}})}^{2} - 4 (4) \Rightarrow {(α - β)}^{2} = \frac{64}{3} - 16 \Rightarrow {(α - β)}^{2} = \frac{64 - 48}{3} = \frac{16}{3} \Rightarrow α - β = \frac{4}{\sqrt{3}} - - - (i i) Solving (i) and (ii) we get α = 2 \sqrt{3} β = \frac{2}{\sqrt{3}} ∴ The roots of the equation is 2 \sqrt{3} and \frac{2}{\sqrt{3}}$

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