quadratic equation - nature of roots For what values of a does the equation $$x^2-( 2^a-1)x-3(4^{a-1}2^{a-2})=0$$ possess real roots? 
Since the roots are to be real that means the discriminant should be $\geq 0$ 
$$\Rightarrow (2^a-1)^2+4\cdot 3\cdot (4^{a-1}2^{a-2}) \geq 0$$

Hint: what are the signs of the terms on the left?
