21. Among the following polynomials, the one with the largest real root is ( ).
(A) $a(x)=x^{19}+2018 x^{11}+1$
(B) $b(x)=x^{17}+2018 x^{11}+1$
(C) $c(x)=x^{19}+2018 x^{13}+1$
(D) $d(x)=x^{17}+2018 x^{13}+1$
(E) $e(x)=2019 x+2018$
21. B.

From the problem, we know that the five functions are all monotonically increasing, and
$$
\begin{array}{l}
a(0)=b(0)=c(0)=d(0)=1>0, \\
e(0)=2018>0, \\
a(-1)=b(-1)=c(-1)=d(-1)<0, \\
e(-1)=-1<0 .
\end{array}
$$

Thus, the unique real root of each polynomial lies in the interval $(-1,0)$. For any number $x$ in this interval and positive odd numbers $a, b (a<b)$, we have $x^{a}<x^{b}$.

Therefore, among the functions $a(x), b(x), c(x), d(x)$, the real root of $b(x)$ is the largest, and the real root of $e(x)$ is
$$
x=-\frac{2018}{2019} \text {. }
$$

Since $b\left(-\frac{2018}{2019}\right)<0$, the real root of $b(x)$ is the largest.