Solve : $x^{3} + 3 x^{2} + 5 x + 3 = 0$

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Solution

$x^{3} + 3 x^{2} + 5 x + 3 = 0$

$x^{3} + 2 x + x + 3 x + 2 x + 3 = 0$

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

Solving the above quadratic equation, we get, $x = - 1 \pm \sqrt{2} i$

The roots of $x^{3} + 3 x^{2} + 5 x + 3 = 0$
are
$x_{1} = - 1$ ,
$x_{2} = - 1 + \sqrt{2} i$ ,
and
$x_{3} = - 1 - \sqrt{2} i$

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