4. Given positive numbers $p, q, a, b, c (p \neq q)$. If $p, a, q$ form a geometric sequence, and $p, b, c, q$ form an arithmetic sequence, then the quadratic equation $b x^{2}-2 a x+c=0$ ( ).
(A) has two equal real roots
(B) has two real roots of the same sign but different values
(C) has two real roots of opposite signs
(D) has no real roots
4. D.

Given, $a^{2}=p q, b+c=p+q$, and $c$ is between $p$ and $q$.
From the discriminant of the equation $b x^{2}-2 a x+c=0$,
$$
\begin{array}{l}
\Delta=4 a^{2}-4 b c=4\left(a^{2}-b c\right) \\
=4[p q-(p+q-c) c]=4(p-c)(q-c)<0,
\end{array}
$$

we know that the equation has no real roots.