Let $P(x)$ be a polynomial. A number $a$ satisfying the equation $P(a) = 0$ is called a root of this polynomial. For polynomials $P(x)$ and $R(x)$ $$\begin{aligned}
&\mathrm{P}(\mathrm{x}) = \mathrm{x}^{2} - 1 \\
&\mathrm{R}(\mathrm{x}) = \mathrm{P}(\mathrm{P}(\mathrm{x}))
\end{aligned}$$ the following equations are given. Accordingly, I. $-1$ II. $0$ III. $1$ which of these numbers are roots of the polynomial $\mathbf{R}(\mathbf{x})$? A) Only I B) Only II C) Only III D) I and III E) II and III
Let $P(x)$ be a polynomial. A number $a$ satisfying the equation $P(a) = 0$ is called a root of this polynomial. For polynomials $P(x)$ and $R(x)$
$$\begin{aligned}
&\mathrm{P}(\mathrm{x}) = \mathrm{x}^{2} - 1 \\
&\mathrm{R}(\mathrm{x}) = \mathrm{P}(\mathrm{P}(\mathrm{x}))
\end{aligned}$$
the following equations are given.
Accordingly,
I. $-1$\\
II. $0$\\
III. $1$
which of these numbers are roots of the polynomial $\mathbf{R}(\mathbf{x})$?
A) Only I\\
B) Only II\\
C) Only III\\
D) I and III\\
E) II and III