The number of integral values of `a` for which `x^2+2ax-3a+10>0` ,` ∀ 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

The number of integral values of x satisfying |x^2-1|leq3 is

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

Number of integral values of 'a' for which (a-1)x^(2)+(a-1)x+1>=0AA x in R ,is ?

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 the quadratic equation x^(2)+(a+19)x+19a+1=0 has integral roots,are

Find the number of integral vaues of 'a' for which the range of function f (x) = (x ^(2) -ax +1)/(x ^(2) -3x+2) is (-oo,oo),