Re: HSC 2012 Marathon :)
Two of the roots of the equation x^3 + ax^2 + b = 0 are reciprocals of each other (a and b are real).
i) show that the third root is equal to -b
ii) show that a= b - 1/b
iii) show that the two roots, which are reciprocals, will be real if -0.5 < = b < = 1/2