If `x^2+2ax+a lt 0 AA x in [1, 2]` then find set of all possible values of a

Find all possible values of sqrt(|x|-2)

Find all possible values of sqrt(|x|-2) .

If the difference between the roots of the equation x^(2)+ax+1=0 is less then sqrt(5) , then find the set of possible value of a .

If the difference between the roots of x^(2) + ax + 1 = 0 is Jess than sqrt(5) then the set of possible values of a is

If x^(2) + 2px - 2p + 8 gt 0 for all real values of x, then the set of all possible values of p is

If the difference between the roots of the equation x^(2)+ax+1=0 is less then sqrt(5) , then the set of possible values of a is