The roots of the equation $3 x^{2} - 4 x + 2 = 0$ are

\frac{1 + \sqrt{2}}{3}

\frac{1 - \sqrt{2}}{3}

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\frac{2 + \sqrt{10}}{3}

\frac{2 - \sqrt{10}}{3}

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\frac{2 + i \sqrt{2}}{3}

\frac{2 - i \sqrt{2}}{3}

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4 + i \frac{\sqrt{2}}{3}

4 - i \frac{\sqrt{2}}{3}

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Solution

The correct option is C $\frac{2 + i \sqrt{2}}{3}$ , $\frac{2 - i \sqrt{2}}{3}$
The given quadratic equation is, $3 x^{2} - 4 x + 2 = 0$
comparing it with standard form quadratic equation $a x^{2} + b x + c = 0$
we get, $a = 3, b = - 4, c = 2$
Thus required roots are given by,
$\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
$= \frac{4 \pm \sqrt{16 - 24}}{6} = \frac{4 \pm 2 \sqrt{- 2}}{6}$
$= \frac{2 \pm \sqrt{2} i}{3}$ since $\sqrt{- 1} = i$

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