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Ans is an option **(B) **

Sum of the roots $=4a+3a=7a=\frac{-b}{1}$ $\Rightarrow$ $b=-7a \quad \longrightarrow (1)$

Product of roots $=4a\times3a=12a^{2}=\frac{c}{1}$ $\Rightarrow$ $c=12a^{2} \quad \longrightarrow (2)$

Squaring $(1)$ and adding to $(2),$ we get $b^{2}+c=61a^{2}$

Among all the options, only $549$ satisfies the above equation with $a$ being an integer i.e. $\pm 3$. In all other cases, $a$ is not an integer.