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

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

The set of values of k for which kx^(2)-x-k+1<0AA x in R, is

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

The set of values of k for which x^(2)+(4k-1)x+9>0AA x in R is

The number of pairs (a,b) for which a(x+1)^2+b(x^(2)-3x-2)+x+1=0 AA x in R is :

The number of pairs (a,b) for which a(x+1)^(2)+b(x^(2)-3x-2)+x+1=0AA x in R

The least natural number a for which x+ax^(-2)>2AA x in(0,oo) is 1(b)2(c)5 (d) none of these

Find the values of k for which |(x^(2)+kx+1)/(x^(2)+x+1)|<2,AA x in R

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:

The quadratic expression ax ^(2)+bx+c gt 0 AA x in R, then :