If set of values `a` for which `f(x)=a x^2-(3+2a)x+6a!=0` is positive for exactly three distinct negative integral values of `x` is `(c , d]` , then the value of `(c^2 4//d)` is equal to ________.

Answer

`(-0.75)`

Explanation

`f(x)=ax^(3)-(3+2a)x+6`
`=(ax-3)(x-2)`

Here, roots of the equation
`f(x)=0` are 2 and 3/a, and f(0)=6.
f(x) should be positive for exactly three negative integral values of x.
Therefore, graph of f(x) must be a downward parabola passing through x=2 and x=3/ and `-4le(3)/(a)lt-3`
`:.ain(-1,(3)/(4)]`
`:.c=-1,d=-(3)/(4)`