$2 \cdot 105$ The roots of the equation $64 x^{3}-144 x^{2}+92 x-15=0$ form an arithmetic sequence, the difference between the largest and smallest root is
(A) 2 .
(B) 1 .
(C) $\frac{1}{2}$.
(D) $\frac{3}{8}$.
(E) $\frac{1}{4}$.
(18th American High School Mathematics Examination, 1967)
The original equation can be transformed into
$$
x^{3}-\frac{9}{4} x^{2}+\frac{23}{16} x-\frac{15}{64}=0 .
$$

Let the three roots of the equation be $a-d, a, a+d$. By Vieta's formulas,
$$
\left\{\begin{array} { l } 
{ ( a - d ) + a + ( a + d ) = \frac { 9 } { 4 } , } \\
{ ( a - d ) a ( a + d ) = \frac { 1 5 } { 6 4 } . }
\end{array} \quad \text { we get } \quad \left\{\begin{array}{l}
a=\frac{3}{4}, \\
d= \pm \frac{1}{2} .
\end{array}\right.\right.
$$

Therefore, $(a+|d|)-(a-|d|)=2|d|=1$.
Hence, the answer is $(B)$.