Suppose a and b are real numbers such that the roots of the cubic equation ax3-x2+bx-1 = 0 are all positive real numbers. Prove that :
(i) 0 < 3ab ≤1
(ii) b≥√3
P.S. I can't believe I missed this ... this one is easy ...
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3 Answers
62Try to use that the derivative of this equation has 2 +ve real roots..
that will give all the things that u want :)
one is derivative +ve
product of roots positive
and sum of roots is +ve..
i think this should give the solution :)
62one thing i missed thoug..
a has to be +ve bcos f(0) is -ve..
so limit to -infinity is -infinity.. other wise there will be a -ve root between -infinity and 0!!
1I did until sum of roots = product of roots.
After that if you use A.M. ≥ G.M. can get the answer ... I forgot about A.M ≥ G.M. in test -.-