Find the square root of following polynomial $(2 x^{2} - 5 x + 2) (3 x^{2} - 5 x - 2) (6 x^{2} - x - 1)$

| (2 x - 1) (x - 2) (3 x + 1) |

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| (2 x - 1) (x + 2) (3 x + 1) |

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| (2 x + 1) (x - 2) (3 x + 1) |

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None of these

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Solution

The correct option is A $| (2 x - 1) (x - 2) (3 x + 1) |$
We find the square root of $(2 x^{2} - 5 x + 2) (3 x^{2} - 5 x - 2) (6 x^{2} - x - 1)$ as shown below:

$= \sqrt{(2 x^{2} - 5 x + 2) (3 x^{2} - 5 x - 2) (6 x^{2} - x - 1)}$

$= \sqrt{(2 x^{2} - 4 x - x + 2) (3 x^{2} - 6 x + x - 2) (6 x^{2} - 3 x + 2 x - 1)}$

$= \sqrt{[2 x (x - 2) - 1 (x - 2)] [3 x (x - 2) + 1 (x - 2)] [3 x (2 x - 1) + 1 (2 x - 1)]}$

$= \sqrt{[(2 x - 1) (x - 2)] [(3 x + 1) (x - 2)] [(3 x + 1) (2 x - 1)]}$

$= \sqrt{(2 x - 1) (x - 2) (3 x + 1) (x - 2) (3 x + 1) (2 x - 1)}$

$= \sqrt{(2 x - 1)^{2} (x - 2)^{2} (3 x + 1)^{2}}$

$= \sqrt{[(2 x - 1) (x - 2) (3 x + 1)]^{2}}$

$= (2 x - 1) (x - 2) (3 x + 1)$

Hence, the square root of $(2 x^{2} - 5 x + 2) (3 x^{2} - 5 x - 2) (6 x^{2} - x - 1)$ is $(2 x - 1) (x - 2) (3 x + 1)$ .

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B

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