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IAT (IISER) 2020
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Let $a, b$ be nonzero real numbers. If $p(x)=x^n+c_{n-1} x^{n-1}+\cdots+c_0$, where $c_{n-1}, \ldots, c_0$ are integers and $n \geq 3$, then which of the following statements is correct?
A
If $a+i b$ is a root of $p(x)$, then $n$ must be even.
B
If $a$ is a root of $p(x)$, then $n$ must be odd.
C
If $a+i b$ is a root of $p(x)$, then $(a+i b)^2$ can never be a root of $p(x)$.
D
If $a$ is a root of $p(x)$, then $a$ must be an integer.
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