Find the zeroes of the polynomial 3x^2-3√3+2 using middle term split

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Solution

3x^2-3√3x+2 = 3x^2-√3x-2√3x+2
=√3x(√3x-1)-2(√3x-1)
=(√3x-1)(√3x-2)
3x^2-3√3x+2 = 0
so (√3x-1)(√3x-2)=0
(√3x-1)=0
√3x=1
x=1/√3
(√3x-2)=0
√3x=2
x=2/√3x

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