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

If the roots of the equation x^2-8x+a^2-6a=0 are real and distinct, then find all possible value of adot

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

Find all possible values of (x^2+1)/(x^2-2) .

If f(x)=sgn(2sinx+a) is continuous for all x , then find the possible values of adot

For x in R , find all possible values of |x-3|-2 (ii) 4-|2x+3|

Consider the equation x^4 + 2ax^3 + x^2 + 2ax + 1 = 0 where a in R . Also range of function f(x)= x+1/x is (-oo,-2]uu[2,oo) If equation has at least two distinct positive real roots then all possible values of a are

If aa n db are positive numbers and eah of the equations x^2+a x+2b=0a n dx^2+2b x+a=0 has real roots, then the smallest possible value of (a+b) is_________.

let f(x)=-x^3+(b^3-b^2+b-1)/(b^2+3b+2) if x is 0 to 1 and f(x)=2x-3 if x if 1 to 3 .All possible real values of b such that f (x) has the smallest value at x=1 ,are

If x lt 2 , then find the values of x^(2) graphically.

If alpha,beta are roots of x^2-3x+a=0 , a in R and alpha <1< beta then find the value of a.