The least value of `alpha in R` for which `4alphax^(2)+(1)/(x)ge1,` for all `xgt0,` is

The least value of alpha in R for which 4ax^2+(1)/(x)ge1 , for all xgt 0 , is

The least value of a in RR " for which " 4ax^(2)+(1)/(x)ge1 " for all" xgt0 , is

The least value of a in R for which 4ax^(2)+(1)/(x)>=1, for all x>0, is

The least value of a in RR for which 4ax^2+1/x >= 1 , for all x > 0 , is

The least value of a in RR for which 4ax^2+1/x >= 1 , for all x > 0 , is

The set of values of p inR for which x^2 +px+ 1/4 (p+2)ge 0 for all x in R is

The set of values of a for which (a - 1) x^(2) - (a + 1) x + a - 1 ge 0 ture for all x ge 2 is

The value of parameter alpha , for which the function f(x) =1+alphax, alpha ne 0 is the inverse of itself is: