(a) For f(x) to be always positive minima of f(x) should be >0 f'(x) = 0 at x = 2a So 4a^2-8a^2+5a^2-6a>0 a^2-6a>0 So a should lie in (-infinity,0) U (6,infinity)
(b) For maximum distance between roots maximise (alpha-beta)^2 = (alpha+beta)^2-4alpha*beta =16a^2-4*(5a^2-6a) =-4a^2+24a This has a maxima at a=3
Krishna Gopal Singh
B.Tech Chemical Engg
IIT Delhi 2002
Currently doing PhD from IIT Delhi
Moderation Team
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