State true or false:
$x = 2$ is a root of $2 x^{3} + x^{2} - 7 x - 6$ .

True

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False

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Solution

The correct option is A True
$p (x) = 2 x^{3} + x^{2} - 7 x - 6.$
Then, $p (2) = 2 (2)^{3} + (2)^{2} - 7 (2) - 6 = 16 + 4 - 14 - 6 = 0$ .
Hence, $x = 2$ is a root of $p (x)$ .
Therefore, it is true and option $A$ is correct.

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State true or false.
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