In the polynomial $f (x) = a_{0} x^{n} + a_{1} x^{n - 1} + . . . + a_{n - 1} x + a_{n}, where a_{0}, a_{1}, a_{2}, . . ., a_{n}$ are the real numbers, if $a_{0} = a_{1} = a_{2} = . . . = a_{n - 1} = 0 and a_{n} \neq 0,$ then this is

Not a polynomial

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A linear polynomial

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A constant polynomial

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A zero polynomial

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Solution

The correct option is C A constant polynomial
$f (x) = a_{0} x^{n} + a_{1} x^{n - 1} + . . . + a_{n - 1} x + a_{n}, where a_{0} = a_{1} = . . . = a_{n - 1} = 0, a_{n} \neq 0$
$∴ f (x) = a_{n} \neq 0, and a_{n} \in R$
$\Rightarrow f (x)$ is a constant polynomial

Hence, the correct answer is option (c).

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n

a_{0}

a^{'} s

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