If $a , b , c \in \mathrm { R }$ and 1 is a root of equation $a x ^ { 2 } + b x + c = 0$, then the curve $y = 4 a x ^ { 2 } + 3 b x + 2 c , a \neq 0$ intersect $x$-axis at\\
(1) two distinct points whose coordinates are always rational numbers\\
(2) no point\\
(3) exactly two distinct points\\
(4) exactly one point