Find the zeros of the polynomial: $x^{3} + 2 x^{2} - x - 2$

1, - 1, - 2

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1, 3, 7

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1, - 2, 4

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None of these

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Solution

The correct option is A $1, - 1, - 2$
The polynomial $x^{3} + 2 x^{2} - x - 2 = 0$ can be factorised as follows:

$x^{3} + 2 x^{2} - x - 2 = 0$
$⟹$ $x^{2} (x + 2) - 1 (x + 2) = 0$
$⟹$ $(x^{2} - 1) (x + 2) = 0$
$⟹$ $x^{2} - 1 = 0$ or $x + 2 = 0$
$⟹$ $x^{2} = 1$ or $x = - 2$
$x = 1$ , $x = - 1$ and $x = - 2$

Hence, the zeroes of the polynomial $x^{3} + 2 x^{2} - x - 2 = 0$ are $1, - 1, - 2$ .

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The zeros of the polynomial $x^{2} + \frac{1}{6} x - 2$ are

(a) -3, 4 (b) $\frac{- 3}{2}, \frac{4}{3}$ (c) $\frac{- 4}{3}, \frac{3}{2}$ (d) none of these

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