Let $A = {x : x is a root of the equation x^{3} + 2 x^{2} - x - 2 = 0}$ and $B = {x : x is a prime divisor of 720},$ then $n (A \times B)$ is

6

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9

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12

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15

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Solution

The correct option is B $9$
$x^{3} + 2 x^{2} - x - 2 = 0 \Rightarrow (x^{2} - 1) (x + 2) = 0 \Rightarrow (x - 1) (x + 1) (x + 2) = 0 ∴ x = 1, - 1, - 2 \Rightarrow A = {- 1, 1, - 2}$

Prime divisors of $720$ are $2, 3, 5.$
$\Rightarrow B = {2, 3, 5} ∴ n (A \times B) = n (A) \times n (B) = 9$

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