JEE Quadratics

Algebra Level 5

$\large f(x)=ax^2 - (3 + 2a)x + 6, \quad a\ne 0$

If the set of values of $a$ for which $f(x)$ is postive for exactly three distinct negative integral values of $x$ is $(c,d]$ , then find the value of $c^2 + 16d^2$ .