17. Let the parabola $C: y=x^{2}$, and the point $Q(20,14)$. A line passing through point $Q$ with a slope of $m$ (where $r<m<s, r, s \in \mathbf{R}$) does not intersect the parabola $C$. Then $r+s=(\quad)$.
(A) 1
(B) 26
(C) 40
(D) 52
(E) 80
17. E.

Let the equation of the line passing through point $Q$ with slope $m (r < m < s, r, s \in \mathbf{R})$ be
$$
y-14=m(x-20) \text {. }
$$

Since the line does not intersect the parabola $C$, we have
$$
x^{2}-m x+20 m-14=0
$$

has no real roots, i.e.,
$$
\Delta=m^{2}-4(20 m-14)=m^{2}-80 m+56<0 \text {. }
$$

Therefore, $r$ and $s$ are the two real roots of the equation $m^{2}-80 m+56=0$.
Thus, $r+s=80$.