2.45 Let $a+b>c>0$ and $|a-b|<c$, then the nature of the roots of the quadratic equation $a^{2} x^{2}+$ $\left(b^{2}+a^{2}-c^{2}\right) x+b^{2}=0$ is
(A) It has two equal roots.
(B) It has no real roots.
(C) It has two unequal roots.
(D) It has real roots.
(E) It is indeterminate.
(Jilin Province Eight Cities Junior High School Mathematics Competition, 1986)
[Solution] Clearly $a \neq 0$, otherwise it would contradict the given conditions $a+b>c>0$ and $|a-b|c>0$,
we know $a+b+c>0, a+b-c>0$.
Also, from $|a-b|0$, we have
$$
a-b+c>0, \quad a-b-c<0 .
$$

Thus $\Delta<0$, the equation has no real roots.
Therefore, the answer is $(B)$.