Question

Find all the value of the parameter 'a' for which the inequality $4^x-a{2}^x-a+3⩽0$ is satisfied by at least one real x

Answer 1

Put $t=2^x$

$t^2-at-a+3=0$

this quadratic should have a +ve root

thus $D=a^2+4(a-3)\ge 0$

$\Rightarrow (a+6)(a-2)\ge 0$

$\Rightarrow a\ge 2$.