If f(x) be a continuous function for all real values of x and satisfies x2+x(f(x)−2)+23−3−3f(x)=0∀x∈R then the value of f(3) is

f3=Ltx→3 x2+2x+23−33−x=21−3

If f(x) be a continuous function for all real values of x and satisfies x2+x(f(x)−2)+23−3−3f(x)=0∀x∈R then the value of f(3) is

f3=Ltx→3 x2+2x+23−33−x=21−3

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$If f (x) be a continuous function for all real values of x and satisfies$ $x^{2} + x (f (x) - 2) + 2 \sqrt{3} - 3 - \sqrt{3} f (x) = 0 \forall x \in R then the value of f (\sqrt{3}) is$

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$2 \sqrt{3} - 1$

$2 (1 - \sqrt{3})$

$2 (\sqrt{3} - 1)$

$\sqrt{3}$

answer is D.

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$f (\sqrt{3}) = \underset{x \to \sqrt{3}}{L t} \frac{x^{2} + 2 x + 2 \sqrt{3} - 3}{\sqrt{3} - x} = 2 (1 - \sqrt{3})$

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If f(x) be a continuous function for all real values of x and satisfies x2+x(f(x)−2)+23−3−3f(x)=0∀x∈R then the value of f(3) is

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$If f (x) be a continuous function for all real values of x and satisfies$ $x^{2} + x (f (x) - 2) + 2 \sqrt{3} - 3 - \sqrt{3} f (x) = 0 \forall x \in R then the value of f (\sqrt{3}) is$