State the following statement is True or False
The zero of the polynomial $x^{3} - 27$ is $3$

True

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False

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Solution

The correct option is A True
Rewrite the polynomial $x^{3} - 27 = 0$ as:

$x^{3} - 27 = 0 \Rightarrow x^{3} - 3^{3} = 0 \Rightarrow (x - 3) (x^{2} + 3 x + 3^{2}) = 0 (∵ a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})) \Rightarrow (x - 3) (x^{2} + 3 x + 9) = 0 \Rightarrow (x - 3) = 0, (x^{2} + 3 x + 9) = 0 \Rightarrow x = 3, x^{2} + 3 x + 9 = 0$

Hence, one of the zeroes of the polynomial $x^{3} - 27$ is $3$ .

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