Find the roots of the equation $2 x^{2} + 4 x + 6 = 0$ .

$- 1 \pm \sqrt{5} i$

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$- 1 \pm \sqrt{7} i$

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$- 1 \pm \sqrt{2} i$

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$- 1 \pm \sqrt{3} i$

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Solution

The correct option is C
$- 1 \pm \sqrt{2} i$

Equation $2 x^{2} + 4 x + 6 = 0$

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

$= \frac{- 4 \pm \sqrt{16 - 4 \times 2 \times 6}}{2 \times 2}$

$= \frac{- 4 \pm \sqrt{(- 32)}}{4}$

$= \frac{- 4 \pm 4 i \sqrt{(2)}}{4}$

$= - 1 \pm \sqrt{2} i$

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