1.
Show that the roots r,s,tr, s, t of the cubic x(x2)(3x7)=2x(x-2)(3x-7) = 2 are real and positive. Also compute the value of tan1(r)+tan1(s)+tan1(t)\tan^{-1}(r) + \tan^{-1}(s) + \tan^{-1}(t).