4. Given positive numbers $p, q, a, b, c$, where $p \neq q$, 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 no real roots
(B) has two equal real roots
(C) has two distinct real roots with the same sign
(D) has two real roots with opposite signs
4. 【Analysis and Solution】Solution 1: Since each option is determined and mutually exclusive, the special value inspection method can be used. Take the geometric sequence $1,2,4$, and the arithmetic sequence $1,2,3,4$, which meet the problem's conditions. Then the equation is $-2 x^{2}-4 x+3=0$ with $\Delta<0$, so the answer is (A).

Solution 2: According to the problem, $a^{2}=p q$. Let the common difference of the arithmetic sequence $p, b, c, q$ be $d(\neq 0)$, and $\Delta=4 a^{2}-4 b c$. From $a^{2}-b c=$ $p q-(p+d)(q-d)=p d-q d+d^{2}=(-3 d) d+d^{2}=-2 d^{2}<0$, we can get $\Delta<0$, so the answer is (A).