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R(1) = 1 - 3 + 2 = 0 \Rightarrow x = 1 \text{ is a root}.
Divide $ R(x) $ by $ x - 1 $ using synthetic division:
\begin{array}{r|rrrr}
& 1 & 0 & -3 & 2 \\
& & 1 & 1 & -2 \\
& 1 & 1 & -2 & 0 \\
So $ R(x) = (x - 1)(x^2 + x - 2) $. Factor the quadratic:
x^2 + x - 2 = (x + 2)(x - 1).
R(x) = (x - 1)^2(x + 2).
The roots are $ x = 1 $ (with multiplicity 2) and $ x = -2 $. Therefore, there are **two distinct real roots**, but **three real roots counting multiplicity**. Since the question asks for the number of real roots (not distinct), the answer is: