Let `f(x)=x^(2)+(a^(2)+3)x+2x+2(a^(2)+3)` is such that it is negative for exactly three integral values of 'x' then greatest integer value of `a^(2)` equals `(a in R)`

The set of values of 'a' for which f(x)=ax^(2)+2x(1-a)-4 is negative for exactly three integral values of x, is-

If set of values a for which f(x)=ax^(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

Let f(x)=x^(2)-ax+3a-4 and g(a) be the least value of f(x) then the greatest value of g(a)

The set of values of 'a' for which ax^(2)-(4-2a)x-8lt0 for exactly three integral values of x, is

Let f(x) = cos^(2) x + cos x +3 then greatest value of f(x) + least value of f(x) is equal to

The values of 'a' for which the quadraic expression ax^(2)+(a-2)x-2 is negative for exactly two integral values of x , belongs to

Let f(x)=(x^(2)+2)/([x]),1 le x le3 , where [.] is the greatest integer function. Then the least value of f(x) is

Let f(x)={(x^3+2x^2,x in Q),(-x^3+2x^2+ax, x !in Q)) , then the integral value of 'a' so that f(x) is differentiable at x=1 is