17・127 The three sides of $\triangle A B C$ are of lengths $a, b, c$. Then the situation of the roots of the quadratic equation $b^{2} x^{2}-\left(b^{2}+c^{2}-a^{2}\right) x+c^{2}=0$ with respect to $x$ is
(A) It has real roots.
(B) It has no real roots.
(C) It has two equal real roots.
(D) It has two unequal real roots.
(Anhui Province, Anqing and other counties and cities Junior High School Mathematics Competition, 1989)
[Solution] From the given, we know the discriminant of the equation is
$$
\begin{aligned}
\Delta & =\left(b^{2}+c^{2}-a^{2}\right)^{2}-4 b^{2} c^{2} \\
& =\left(b^{2}+c^{2}-a^{2}+2 b c\right)\left(b^{2}+c^{2}-a^{2}-2 b c\right) \\
& =\left[(b+c)^{2}-a^{2}\right]\left[(b-c)^{2}-a^{2}\right] \\
& =(b+c+a)(b+c-a)(b-c+a)(b-c-a), \\
& \because \quad b+c+a>0, \quad b+c>a, \quad b+a>c, \quad c+a>b,
\end{aligned}
$$
$\therefore \quad \Delta<0$, so the equation has no real roots.
Therefore, the correct choice is (B).