The number of integral values of `a` for which `x^(2)+2ax-3a+10>0AA x in R`

The number of integral values of a for which x^(2) - (a-1) x+3 = 0 has both roots positive and x^(2) + 3x + 6 - a = 0 has both roots negative is

find a for which 3x^(2) + ax+3 gt 0,AA x in R.

Find the number of integral values of 'a' for which ax^2 - (3a + 2)x + 2(a + 1) < 0, a != 0 holds exactly four integral value of x.

The number of integral values of a for which f(x) = x^3 + (a + 2)x^2 + 3ax + 5 is monotonic in AA x in R

find a for which ax^(2) + x -1lt 0,AA x in R ?

The number of integer values of a for which x^2+ 3ax + 2009 = 0 has two integer roots is :

Find the number of positive integral values of k for which kx ^(2) +(k-3)x+1 lt 0 for atleast one positive x.

The number of integral values of k for which the inequality x^(2)-2(4k-1)x+15k^(2)-2k-7 ge0 hold for x in R are _____________

Let f (x) = (x+5)/(sqrt(x^(2) +1) ) , then the smallest integral value of k for which f (x) le k AA x in R is

The sum of all intergral values of lamda for which (lamda^(2) + lamda -2) x ^(2) + (lamda +2) x lt 1 AA x in R, is: