Explanation

(c)
Given $bx + cx + a = 0$ has imaginary roots
$\Rightarrow c^{2} - 4ab < 0$
$\Rightarrow c^{2} < 4ab$
$\Rightarrow \ - c^{2} > - 4ab$ ...(i)
Let $f(x) = 3b^{2}x^{2} + 6bcx + 2c^{2}$
Here, $3b^{2} > 0$
So, the given expression has a minimum value
$\therefore$ Minimum value$= \frac{- D}{4a}$
$= \frac{4ac - b^{2}}{4a}$
$= \frac{4\left( 3b^{2} \right)\left( 2c^{2} \right) - 36b^{2}c^{2}}{4(3b^{2})}$
$= - \frac{12b^{2}c^{2}}{12b^{2}} = - c^{2} > - 4ab$
[from Eq. (i)]