The least value of `a in RR` for which `4ax^2+1/x >= 1`, for all `x > 0`, 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 alpha in R for which 4alphax^(2)+(1)/(x)ge1, for all xgt0, is

The least integral value of 'k' for which (k -2)x^2 +8x+k+4>0 for all xepsilonR, is:

The least integral value of 'k' for which (k -2)x^2 +8x+k+4>0 for all xepsilonR , is:

The value of a for which the equation x^3 + ax + 1 = 0 and x^4+ ax + 1 = 0 have a common root, is

Find all numbers a for each of which the least value of the quadratic trinomial 4x^2 - 4ax + a^2 - 2a + 2 on the interva 0 le x le 2 is equal to 3.