Solve the following equation:
$x^{3} + 63 x - 316 = 0$ .

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Solution

Given equation, $x^{3} + 63 x - 316 = 0$

$⟹ x^{3} + 4 x^{2} - 4 x^{2} + 79 x - 16 x - 316 = 0 ⟹ (x - 4) (x^{2} + 4 x + 79) = 0$

Solving the quadratic equation, we have $x = - 2 \pm 5 \sqrt{3} i$

$∴$ Roots of the given equation are $x = 4, - 2 \pm 5 \sqrt{3} i$

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