I've probably done something wrong but here goes...
Using standard formula we get roots to be
Since roots are real and unequal,
Canceling we get
But when the inequality is raised to 2 must we not have that b>0 ,otherwise the inequality may change if b<0.The problem assumes only .
Example:take b=-3 and a=1 :we have ,but
Split it up into two cases then.
So let case 1 be
which was my first post and hence .
Case 2 is
and hence .
From which we get that...
Although I haven't checked I think some of the the > can be replaced with for one of the cases to include with . (This will only happen when b is negative since if b is +ve then )