I've probably done something wrong but here goes...
Using standard formula we get roots to be
.
Since roots are real and unequal,
Hence...
.
Canceling we get
...
Hence result.
If i understand you correctly :from you get ,by raising 1st the inequality to the power of 2 and then multplying by 16.
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
Yeah you're right.
Split it up into two cases then.
we know.
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 )