The roots of the equation $x^{3} - 5 x^{2} - 2 x + 24 = 0$ , are

- 2, - 3, 4

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- 2, 3, 4

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- 2, 3, - 4

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2, - 3, - 4

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Solution

The correct option is C $- 2, 3, 4$
Let $f (x) = x^{3} - 5 x^{2} - 2 x + 24$
Then $f (- 2) = {(- 2)}^{3} - 5 {(- 2)}^{2} - 2 (- 2) + 24 = 0$
Gives $(x + 2)$ is one roots and given equation can be written as
$(x + 2) (x^{2} - 7 x + 12) = 0$
$\Rightarrow (x + 2) (x - 3) (x - 4) = 0$
Hence, roots are $- 2, 3, 4$ .

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