quadratic equation - nature of roots

Question

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 $\geq 0$ $$\Rightarrow (2^a-1)^2+4\cdot 3\cdot (4^{a-1}2^{a-2}) \geq 0$$

Answer 1

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