Let a, b be nonzero real numbers. If p(x)=x^n+c_ n-1 x^ n-1 + +c₀ , where c_ n-1 , , c₀ are integers and n 3 , then which of the following statements is correct?

Options

1. AIf a is a root of p(x) , then n must be odd.
2. BIf a+i b is a root of p(x) , then (a+i b)^2 can never be a root of p(x) .
3. CIf a+i b is a root of p(x) , then n must be even.
4. DIf a is a rational root of p(x) , then a must be an integer.