Find all the values of the parameter a for which the inequality `a9^(x)+4(a-1)3^(x)+agt1` is satisfied for all real values of `x`.

Find all values of the parameter a for which the inequality a.9^x +4(a-1)3^x+a gt 1 is satisfied for all real values of x

Find all the values of the parameter 'a' for which the inequality 4^x-a2^x-a+3 <= 0 is satisfied by at least one real x.

For what values of a is the inequality (x^(2) +ax-2)/( x^(2) -x+1) lt 2 satisfied for all real values of x?

If t is a real number satisfying the equation 2t^3-9t^2+30-a=0, then find the values of the parameter a for which the equation x+1/x=t gives six real and distinct values of x .

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....

Find the values of the parameter a for which the roots of the quadratic equation x^(2)+2(a-1)x+a+5=0 are not real

Sum of the squares of all integral values of a for which the inequality x^(2) + ax + a^(2) + 6a lt 0 is satisfied for all x in ( 1,2) must be equal to

Find all the values of p for which the equation x^(4)-4x^(3)-8x^(2)+p=0 has two real solutions

Find the values of the parameter a for which the roots of the quadratic equation x^(2)+2(a-1)x+a+5=0 are real and distinct

Find the values ' a ' for which the function f(x)=(a+2)x^3-3a x^2+9a x-1 decreases for all real values of x .