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

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

The least integral value of x for which 33 - x(2 + 3x) gt 0 is

Let f : R rarr R and g : R rarr R be two given functions defined as f(x) = 3x^(2) + 2 and g(x) = 3x-1, AA x in R Then find [(gof)(x)] at x = 1.

Find the least integral value of 'k' for which the quadratic polynomial (k-1)x^(2) + 8x + k + 5 gt 0 AA x in R

the area of region for which 0 lt y lt 3 - 2x-x^2 and x gt 0 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 quadratic expression ax ^(2)+bx+c gt 0 AA x in R, then :

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

If g (x) = x ^(2) -1 and gof (x) = x ^(2) + 4x + 3, then f ((1)/(2)) is equal (f(x) gt 0 AA x in R)

A function f is defined by f(x^(2) ) = x^(3) AA x gt 0 then f(4) equals