Subjective Type

Solve the following equation: $$x^{3} + 21x + 342 = 0$$.

Solution

Given equation, $$x^3+21x+342=0$$

$$\Rightarrow x^3 - 6x^2 + 6x^2 + 57x -36x + 342 = 0$$

$$\Rightarrow (x+6)(x^2-6x+57) = 0$$

Hence, $$x+6=0$$ and $$x^2-6x+57=0$$

Therefore, $$ x= -6 \,\,\text{and} \,\, x = \dfrac{6\pm\sqrt{36-4\times57}}{2} = 3\pm4\sqrt{3}i$$

Thus roots of the given equation are $$x = -6, 3\pm4\sqrt{3}i $$

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