I think option C is correct,<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />
see, if we solve it like a quad. ,we get the answer k belongs to(-INFINITY,4] and if solved by trigonometrically we get k belongs to all real,combining these we get k belongs to(-INFINITY,4] .
Lokesh,your answer is correct.But I think we can solve this only by trigonometry .How have you solved it by quadratic?I have done it like this:I have divided both sides by [k2-9]1/2.This is standard form and can be converted to sin or cos completely and we know that sin or cos has to lie between -1 and 1.So,-1<=k+1/[k2-9]1/2<=1.