If the inequality `x^2 + kx +k < 0` is satisfied for at least one real x, then find the smallest positive interaer value of k.

if allvalues of x which satisfies the inequality log _((1//3))(x ^(2) +2px+p^(2) +1) ge 0 also satisfy the inequality kx ^(2)+kx- k ^(2) le 0 for all real values of k, then all possible values of p lies in the interval :

if allvalues of x which satisfies the inequality log _((1//3))(x ^(2) +2px+p^(2) +1) ge 0 also satisfy the inequality kx ^(2)+kx- k ^(2) le 0 for all real values of k, then all possible values of p lies in the interval :

If the inequality (x^(2)-kx-2)/(x^(2)-3x+4)>-1 for every x in R and S is the sum of all integral values of k, If the inequalitythen find the value of S^(2)

The number of integral values of K the inequality |(x^2+kx+1)/(x^2+x+1)|<3 is satisfied for all real values of x is....

The number of integral values of K' the inequality |(x^2+kx+1)/(x^2+x+1)|<3 is satisfied for all real values of x is....

The number of integral values of K the inequality |(x^(2)+kx+1)/(x^(2)+x+1)|<3 is satisfied for all real values of x is...]|

The number of integral values of K' the inequality |(x^2+kx+1)/(x^2+x+1)|<3 is satisfied for all real values of x is....

The number of integral values of K' the inequality |(x^2+kx+1)/(x^2+x+1)|<3 is satisfied for all real values of x is....

For what values of k is the inequality x^(2)-(k-3)x-k+6>0 valid for all real x?