Question 123
Let $P(x) = a_{2016}x^{2016} + a_{2015}x^{2015} + \dots + a_1x + a_0$ be a degree $2016$ polynomial, where its coefficients satisfy
$$
|a_1 + a_3 + \dots + a_{2015}| \gt |a_0 + a_2 + \dots + a_{2016}|.
$$
Prove that the number of roots of $P(x)$ with absolute value less than $1$ is odd (roots are counted with multiplicity).
$$
|a_1 + a_3 + \dots + a_{2015}| \gt |a_0 + a_2 + \dots + a_{2016}|.
$$
Prove that the number of roots of $P(x)$ with absolute value less than $1$ is odd (roots are counted with multiplicity).