Question

Find the zeroes of the polynomial 4 root 3x square -2 root 3 x - 2 root 3

Answer 1

4√3x^2-2√3x-2√3=0

taking √3 common

4x^2-2x-2=0

4x^2+2x-4x-2=0

2x(2x+1)-2(2x+1)=0

(2x-2)(2x+1)=0

x=-1/2

and x=1

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Answer 2

$4 \sqrt{3} {x}^{2} - 2 \sqrt{3} x - 2 \sqrt{3} = 0 \\ \sqrt{3} (4 {x}^{2} - 2x - 2) = 0 \\ 4 {x}^{2} - 2x - 2 = 0 \\ 4 {x}^{2} - 4x + 2x - 2 = 0 \\ 4x(x - 1) + 2(x - 1) = 0 \\ (4x + 2)(x - 1) = 0 \\ x = \frac{ - 2}{4} = \frac{ - 1}{2} \\ x = 1$

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