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Question

Solve the following equations:
$2 x^{3} + 3 x^{2} + 3 x + 1 = 0$ .

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Solution

Given equation, $2 x^{3} + 3 x^{2} + 3 x + 1 = 0$

$⟹ 2 x^{3} + 2 x^{2} + x^{2} + 2 x + x + 1 = 0 ⟹ (2 x + 1) (x^{2} + x + 1) = 0$

Solving the 2 equations, we have $x = \frac{- 1}{2}, \frac{- 1 \pm \sqrt{3} i}{2}$

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